- “I've fallen for [Jolyne]. From the first time I saw her, completely. And now, to go to the punishment ward for her father... her determination completely won me over. If I can protect her until the end... I'm going to marry her.”
- — Narciso Anasui, Stone Ocean Chapter 59: His Name Is Anasui
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Upon first interacting with Jolyne, he becomes enamored with her. Throughout the series, as they become friends, Anasui often openly flirts with Jolyne and asserts he must marry her, while she ignores or repels his advances. They are somewhat intimate with one another, Jolyne sleeping on Anasui's shoulder in a car, while Anasui laments thinking she's cute.
In the end of Stone Ocean, while original-universe Jolyne and Anasui are never officially together, their counterparts in a newly-created alternate reality (Irene and Annakiss) are referred to as being partners.
Jolysui as a somewhat canon relationship is celebrated by fans. This ship is popular in part that Anasui is often interpreted as transgender, since he takes a much more feminine form in his first appearance, but changes to a masculine one later. Hirohiko Araki states that with Anasui he wanted to "portray a character with an androgynous image that went beyond the standard definition of genders".
The ship is essentially treated as canon, especially since Hirohiko Araki's way of portraying alternate-universe versions of characters often includes similar threads of fate, especially in terms of having similar relationships to others throughout universes.