  By invoking the reflection functors introduced by Bernstein, Gelfand, and
Ponomarev in 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 $\ell^1$-bottleneck distance between their respective
persistence diagrams.
