So... is Air Master finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: October 01, 2003
Manga finished: March 10, 2006
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Air Master follows Aikawa Maki, a young woman who has traded the world of competitive gymnastics for the brutal arena of street fighting.
She's not just fighting for money or fame; violence is the only thing that truly ignites her passion and makes her feel alive.
Using her incredible acrobatic skills and raw power, Maki takes on a variety of challenging opponents, each fight pushing her limits and solidifying her reputation as the formidable "Air Master."
The anime chronicles her journey through the underground fighting scene, exploring her motivations and the reasons behind her chosen path.