On any graph manifold, all transitive pseudo-Anosov flows have at most finitely many orbit-equivalence classes after lifting to a single finite cover, and a new complete bar code invariant decides when glued flows are orbit equivalent.
Flots d' A nosov sur les vari\'et\'es graph\'ees au sens de W aldhausen
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Uniqueness of gluings and virtual finiteness of pseudo-Anosov flows on graph manifolds
On any graph manifold, all transitive pseudo-Anosov flows have at most finitely many orbit-equivalence classes after lifting to a single finite cover, and a new complete bar code invariant decides when glued flows are orbit equivalent.