We describe an interaction of a pseudo-Anosov flow with possible Seifert fibered pieces in the torus decomposition of the underlying manifold: if the fiber is associated to a periodic orbit of the flow, we produce a standard form for the flow in the piece which is a neighborhood of finitely many weakly embedded Birkhoff annuli. A Birkhoff annulus is an annulus so that each boundary component is a closed orbit of the flow and the flow is transverse to the interior of the annulus. Using collections of Birkhoff annuli as a skeleton for some flows, we then produce a very large class of new examples of pseudo-Anosov flows in graph manifolds. This is joint work with Thierry Barbot.