  We study distances on zigzag persistence modules from the viewpoint of
derived categories and Auslander--Reiten quivers. The derived category of
ordinary persistence modules is derived equivalent to that of arbitrary zigzag
persistence modules, depending on a classical tilting module. Through this
derived equivalence, we define and compute distances on the derived category of
arbitrary zigzag persistence modules and prove an algebraic stability theorem.
We also compare our distance with the distance for purely zigzag persistence
modules introduced by Botnan--Lesnick and the sheaf-theoretic convolution
distance due to Kashiwara--Schapira.
