  In this article we analyze totally periodic pseudo-Anosov flows in graph
three manifolds. This means that in each Seifert fibered piece of the torus
decomposition, the free homotopy class of regular fibers has a finite power
which is also a finite power of the free homotopy class of a closed orbit of
the flow. We show that each such flow is topologically equivalent to one of the
model pseudo-Anosov flows which we constructed in a previous article. A model
pseudo-Anosov flow is obtained by glueing standard neighborhoods of Birkhoff
annuli and perhaps doing Dehn surgery on certain orbits. We also show that two
model flows on the same graph manifold are isotopically equivalent (ie. there
is a isotopy of the manifold mapping the oriented orbits of the first flow to
the oriented orbits of the second flow) if and only if they have the same
topological and dynamical data in the collection of standard neighborhoods of
the Birkhoff annuli.
