This is joint work with Thierry Barbot. A graph manifold is an irreducible manifold so that all pieces of the torus decomposition are Seifert fibered. We consider pseudo-Anosov flows in graph manifolds so that all pieces are periodic. This means that a regular fiber is freely homotopic to a closed orbit of the flow. We show that these flows are rigid, that is, they are completely determined up to topological conjugacy by the dynamics and the topological structure of a finite collection of dynamical spines associated to the flow. Each spine is made up of finitely many Birkhoff annuli which contain all dynamical information in the particular Seifert piece of the torus decomposition.