  We prove a classification theorem for transitive Anosov and pseudo-Anosov
flows on closed 3-manifolds, up to orbit equivalence.
  In many cases, flows on a 3-manifold $M$ are completely determined by the set
of free homotopy classes of their (unoriented) periodic orbits. The exceptional
cases are flows with a special structure in their orbit space called a ``tree
of scalloped regions"; in these cases the set of free homotopy classes of
unoriented periodic orbits together with the additional data of a choice of
sign for each $\pi_1(M)$-orbit of tree gives a complete invariant of orbit
equivalence classes of flows.
  The framework for the proof is a more general result about \emph{Anosov-like
actions} of abstract groups on bifoliated planes, showing that the
homeomorphism type of the bifoliation and the conjugacy class of the action can
be recovered from knowledge of which elements of the group act with fixed
points.
  As a consequence, we show that Anosov flows are determined up to orbit
equivalence by the action on the ideal boundary of their orbit spaces, and more
generally that transitive Anosov-like actions on bifoliated planes are
determined up to conjugacy by their actions on the plane's ideal boundary: any
conjugacy between two such actions on their ideal circles can be extended
uniquely to a conjugacy on the interior of the plane.
