Saint Seiya: Canon & Non Canon

The universe of San Seiya what can be considered Canonical and Non-Canonical in the Galaxian Myth.

Saint Seiya
This is the simplest thing to explain, and what should be by far the most obvious. Needless to say, the Classic Manga is canonical, as it is the original storyline which gave birth to the franchise that is known today.

Next Dimension
Saint Seiya: Next Dimension is also canonical as it is the Classic Manga's direct sequel, as was directly stated in Vol. 1:

エリシオンにおける星矢と冥王ハーデスの激闘より遡ること二百四十数年前…. 熱き友情で結ばれた二人の少年の絆を引き裂き、もう一つの聖戦が始まろうとしていた!! 過去と現在が交錯する新たなる銀河神話、「聖闘士星矢」の正統なる続編が始動!!

Over 240 Years before the confront of Seiya and Hades at Elysion, the passionate bonds of friendship of two youths are separated, another Holy War is about to begin!! Past and present intertwine in a new Galaxian Myth, the legitimate sequel of Saint Seiya is about to begin!!.

Saint Seiya: Episode G & Episode G: Assassin
By far the most controversial of all Saint Seiya series, Episode G is an installment whose canonicity has been debated ever since its inception. Here I will attempt to demonstrate all sources that state it's status as either canon or non-canon:

In a Interview at Champion Red No.1, 2003, Masami Kurumada explains his intentions with the release of Episode G:

(http://www.saintseiyapedia.com/wiki/Interviews/Champion_RED_200301/Masami_Kurumada)

Q: Saint Seiya Episode G arrived as a true surprise. Why are you starting Episode G now?

Kurumada: My answer shall be the same as the one George Lucas has given in regards to the production of his Stars Wars Episode I. A conductive environment to the materialization of what I already imagined has simply arrived. With the context of a film, this refers to digital imaginary and new technologies, for a manga it means the new circumstances of the environment.

So Masami Kurumada's intentions with the creation of Episode G was to make a prequel, akin to Star Wars's The Phantom Menace. Not a non-canon Spin-Off.

Continuing, in December of 2003 Masami Kurumada had an interview with the French Magazine Anime Land #97, where he talked about Episode G:

AL: Besides the series Ring ni Kakero 2, which you write and draw yourself, in 2002 you brought us the beginning of Saint Seiya Episode G, drawn by Megumu Okada, and also the new saga of Fuma no Kojira, drawn by your direct disciple Satoshi Yuri. Can you tell us more about these projects? MK: I develop a supervision over them, however the artists are totally free to develop the plot. Megumu Okada has made a trully impressive work, but he prints on it his own style and story. Satoshi Yuri is very responsible and works very seriously. He is my student, we work on the same studio, therefore I can take more of my time with his work than with Episode G.

So Masami Kurumada supervises mangas based on his original work, and the only reason he didn't dedicate more time to Episode G was that he was handling multiple manga.

Continuing...

http://seiya30th.com/series.html

An official Saint Seiya website lists Masami Kurumada as being directly involved in the making of Episode G:

原案は車田正美、作画は岡田芽武.

Or:

Original Draft by Masami Kurumada, drawings by Megumu Okada.

And as one last proof:

http://chancro.jp/comics/assassin

The website that publishes the Episode G: Assassin Webcomic describes it as:

世界を席巻する伝説の超ヒット作「聖闘士星矢」の正統外伝！

Or:

The legendary super hit series "Saint Seiya" dominates the world with a new legitimate gaiden!

In both the previously posted Next Dimension Scan and the above line, the japanese word 正統 (Seitō) is mentioned, and it means Orthodox / Legitimate, in this case stating that something is original / canon.

There are absolutely 0 arguments to claim that Saint Seiya: Episode G is Non-Canon.

Saint Seiya: Saintia Sho
Saintia Sho is, by comparison with Episode G, far easier to explain. Two interviews give explicit evidence regarding it's canonical status. The first one is Chimaki Kuori's interview with the French Magazine La Monde, at Japan Expo 2016:

http://taizen-saintseiya.com/entrevistas/chimaki-kuori-le-monde-2016/

Le Monde: What was your main challenge in the creation of a feminine series about "Saint Seiya", a primarily masculine universe?

Chimaki Kuori: The decision of accepting it was already certain. It meant launching myself into an exhaustive work, and facing the critical eyes of fans used to a canonical universe extremely known and appreciated, without being sure of how they'd receive this reinterpretation. (...) Obviously the male characters reappear, because the series takes place in the same world as the original.

Not convinced yet? Okay. Chimaki Kuori also answered live questions at the place, and while there was no filming, a french Saint Seiya fan named Guillaume Boutet wrote a summary on it:

http://www.actuabd.com/Japan-Expo-2016-Chimaki-Kuori

They then asked her about the manga's creation process, about its relation with Kurumada and the difficulty of writing a story supposedly parallel to the original. Chimaki then remembered Kurumada's own words: "If the story is good, you can accept and ignore some things. The important is to have a good rhythm and for you to have enjoyment in reading the series." She tells that, in the beginning of the project, the idea of focusing on women serving Athena came from Kurumada, some years ago when he was hospitalized. It took some years for the idea to mature, and when Chimaki Kuori was contact, he gave her a general draft to follow, with no duration or number of volumes programmed. If she could finish the progressing story, he'd already be happy.

About the enchange of ideas with Kurumada, Chimaki Kuori reveals that with every new story arc she would send him the script, who would read it all. Kurumada gave her relative freedom, dedicating himself specially in controlling that the series would maintain the "Saint Seiya" spirit. When a fan asked her if she followed the anime or manga to create Saintia Sho, she answered that she greatly enjoyed the anime, but that it had already tried everything. From the anime film, came Eris, the Goddess of Discord, and her becoming the antagonist of Saintia Sho. Chimaki Kuori said that she "pretended the movie to have never happened". The choice of Eris was done by Kurumada, just like the idea of making the story's cast as feminine as possible, and a lot became related to the anime movie because it was the film with which Kurumada had been involved the most at the time.

So, it's very, explicitly obvious that Saintia Sho is set within the Classic Manga's world, functioning as a parallel story, and that the project derives from Masami Kurumada himself, who is greatly involved in the creative process as a supervisor. I can safely consider it canon as well.

Saint Seiya: Lost Canvas
Preview of urgent announcement! Another creation of Seiya...! "Saint Seiya The Lost Canvas Meiou Shinwa"

From NEXT DIMENSION to THE LOST CANVAS,

Kurumada's DNA is now passed to here!!!

Creation: Masami Kurumada

Manga: Shiori Teshirogi A new series!

For the first time in history, a "Multi-Angle-Dual" series, with two Cosmos from two angles a "Myth of Hades" (Meiou Shinwa) is drawn!!

Originally, both Next Dimension and Lost Canvas were sold as two different, yet equally valid interpretations of the same story.

The closest any source has ever come to calling it "Non-Canonical" was the Princess Gold Magazine, which said this:

AnotherStory 設定を共有しながら展開されるアナザーストーリーとして人気をめた作 Or

A popular work in the form of Another Story expands, while at the same time sharing concepts [With Next Dimension]

Finally, there is this Interview with Shiori Teshirogi for the French Website Unificationfrance

http://www.unificationfrance.com/?26635-Cartoonist-2013-Shiori-Teshirogi&lang=fr

Did Saint Seiya have a particular impact in your career?

Yes, but aside from Saint Seiya, all works from Masami Kurumada influenced my career.

How did you arrive at The Lost Canvas?

A long time ago, I went to an autograph session of Masami Kurumada. When I met him, I gave him one of my already published manga and said: "I became a professional artist thanks to you who influenced my career." I thought things would end there, but years after he made contact with me saying he had read my manga. He found them excellent and offered me to write his new Saint Seiya manga. And that's how it went. It was really extraordinary.

Masami Kurumada was personally involved in writing The Lost Canvas

When Lost Canvas began he just gave me a list of key scenes and events to follow with the plot, and told to use them as basis for my own script. As Lost Canvas lasted more than expected, I ended up quickly finishing this list, and so Kurumada-Sensei told me "There's no problem Teshi, I'll let you do whatever you want from now on. You have total freedom."

This confirms that The Lost Canvas, much like other manga in the Franchise, are projects coming from Masami Kurumada himself. Rather than completely separate, Non-Canonical works.