  Multivector fields provide an avenue for studying continuous dynamical
systems in a combinatorial framework. There are currently two approaches in the
literature which use persistent homology to capture changes in combinatorial
dynamical systems. The first captures changes in the Conley index, while the
second captures changes in the Morse decomposition. However, such approaches
have limitations. The former approach only describes how the Conley index
changes across a selected isolated invariant set though the dynamics can be
much more complicated than the behavior of a single isolated invariant set.
Likewise, considering a Morse decomposition omits much information about the
individual Morse sets. In this paper, we propose a method to summarize changes
in combinatorial dynamical systems by capturing changes in the so-called
Conley-Morse graphs. A Conley-Morse graph contains information about both the
structure of a selected Morse decomposition and about the Conley index at each
Morse set in the decomposition. Hence, our method summarizes the changing
structure of a sequence of dynamical systems at a finer granularity than
previous approaches.
