So... is Arakawa Under the Bridge finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: December 27, 2010
Manga finished: July 03, 2015
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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Arakawa Under the Bridge
荒川アンダー ザ ブリッジ
Anime - Base
Release date: April 05, 2010
Arakawa Under the Bridge x Bridge
荒川アンダー ザブリッジ×ブリッジ
Anime - Sequel
Release date: October 04, 2010
Synopsis
Kou Ichinomiya, a man fiercely independent due to his family's motto, finds himself in an unexpected predicament: owing his life to a mysterious homeless girl named Nino who lives under Arakawa Bridge.
Unable to accept this debt, Kou attempts to repay her, but Nino's request is far from conventional. She asks him to be her boyfriend, forcing Kou to abandon his privileged life and join the quirky community living beneath the bridge.
This marks the beginning of Kou's bizarre and transformative journey, as he navigates the eccentric world of the Arakawa riverbank and learns to adapt to a life completely different from anything he's ever known.