  In [Orbit equivalences of pseudo-Anosov flows, arXiv:2211.10505], it was
proved that transitive pseudo-Anosov flows on any closed 3-manifold are
determined up to orbit equivalence by the set of free homotopy classes
represented by periodic orbits, provided their orbit space does not contain a
feature called a "tree of scalloped regions." In this article we describe what
happens in these exceptional cases: we show what topological features in the
manifold correspond to trees of scalloped regions, completely classify the
flows which do have the same free homotopy data, and construct explicit
examples of flows with the same free homotopy data that are not orbit
equivalent.
