Explore quantitative recurrence properties in Z-extension of Axiom A flows on Riemannian manifolds in this 55-minute conference talk from the Workshop on "Rare Events in Dynamical Systems" at the Erwin Schrödinger International Institute. Delve into the asymptotic behavior of first return times to small neighborhoods of starting points, examining almost everywhere convergence and convergence in distribution with respect to probability measures absolutely continuous to infinite invariant measures. Discover how these findings apply to geodesic flows on Z-cover of compact smooth surfaces with negative curvature, providing valuable insights into dynamical systems and mathematical physics.