  We prove a structure theorem for pseudo-Anosov flows restricted to Seifert
fibered pieces of three manifolds. The piece is called periodic if there is a
Seifert fibration so that a regular fiber is freely homotopic, up to powers, to
a closed orbit of the flow. A non periodic Seifert fibered piece is called
free. In a previous paper [Ba-Fe1] we described the structure of a
pseudo-Anosov flow restricted to a periodic piece up to isotopy along the flow.
In the present paper we consider free Seifert pieces. We show that, in a
carefully defined neighborhood of the free piece, the pseudo-Anosov flow is
orbitally equivalent to a hyperbolic blow up of a geodesic flow piece. A
geodesic flow piece is a finite cover of the geodesic flow on a compact
hyperbolic surface, usually with boundary. In the proof we introduce almost
k-convergence groups and prove a convergence theorem. We also introduce an
alternative model for the geodesic flow of a hyperbolic surface that is
suitable to prove these results, and we carefully define what is a hyperbolic
blow up.
