  In this paper we study a certain regularity property of Axiom A flows over
basic sets related to diameters of balls in Bowen's metric, which we call
regular distortion along unstable manifolds. The motivation to investigate the
latter comes from the study of spectral properties of Ruelle transfer
operators. We prove that if the bottom of the spectrum of the tangent map of
the flow over unstable manifolds is point-wisely pinched and integrable, then
the flow has regular distortion along unstable manifolds over the basic set. In
the process, under the same conditions, we show that locally the flow is
Lipschitz conjugate to its linearization over the `pinched part' of the
unstable tangent bundle.
