The reflection distance between zigzag persistence modules

By invoking the reflection functors introduced by Bernstein et al. (Russ Math Surv 28(2):17–32, 1973 ), in this paper we define a metric on the space of all zigzag modules of a given length, which we call the reflection distance. We show that the reflection distance between two given zigzag modules of the same length is an upper bound for the ℓ ^1 -bottleneck distance between their respective persistence diagrams.