So... is Aoi Hana finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 10, 2009
Manga finished: July 06, 2013
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Aoi Hana tells the story of Fumi and Akira, childhood friends who are reunited after years apart when Fumi returns to her hometown for high school. Their renewed friendship is complicated by the changes they've both experienced, and the challenges of navigating their new high school lives.
Fumi, initially overwhelmed by her new surroundings and attention from an older student, struggles to find her own identity and rely less on Akira for support.
Meanwhile, Akira hopes to rekindle the close bond they once shared, but must also respect Fumi's need to grow as an individual. The anime explores themes of friendship, self-discovery, and the complexities of relationships as they navigate the trials of adolescence.