Fried–Christy–Ghys conjecture on almost equivalence of transitive Anosov flows

Let $M$ be a closed orientable $3$-manifold, and let two transitive Anosov flows on $M$ have orientable stable and unstable foliations. They are almost equivalent when, after reparametrization, a homeomorphism identifies the flows in the complement of finitely many closed orbits.

Fried–Christy–Ghys conjecture. Any two transitive Anosov flows with orientable stable and unstable foliations are almost equivalent.

This conjecture predicts that, up to reparametrization and homeomorphism away from finitely many closed orbits, transitive Anosov flows with orientable stable and unstable foliations have the same dynamics. The paper proves the corresponding almost-equivalence statement for transitive Anosov flows on graph manifolds, while the general conjecture remains open.