Przytycki's strong-transversality conjecture for coverings

Let $f$ be a covering map. It satisfies axiom A and the strong transversality condition when its non-wandering set is locally maximal, its non-wandering set is the union of a hyperbolic set on which $f$ acts bijectively with a repulsive set, and the stated multi-transversality condition holds for stable and unstable manifolds. Przytycki's strong-transversality conjecture. The $C^1$-structurally stable coverings are those which satisfy axiom A and the strong transversality condition. The source presents this as a generalization of a conjecture of Przytycki and gives no resolution status.