Ghys’s almost-orbit-equivalence conjecture

Prove that any two transitive Anosov flows with orientable invariant foliations become orbit equivalent after removing finite collections of periodic orbits from the respective flows.

Background

The paper states that Ghys’s conjecture is open in full generality, while it is known for suspensions of toral automorphisms. The authors translate it into a connectivity statement for an ancestry graph of veering triangulations and provide computational evidence.