The operator renewal-type approach to obtain polynomial mixing rates in various innite measure-preserving dynamical systems requires that the tails of a certain inducing scheme have regular variation. An almost Anosov dieomorphism is a dieomorphism (in our case on the 2-torus) that satises the Anosov properties except at a nite set of neutral saddle points. In this invertible setting, the regular varia- tion of the tails has been treated only in very specic settings and/or with unsatisfactory estimates. In this talk I want to present a new methods which works in much greater generality and gives much more precise estimates. The mixing results additionally require the use of an anisotropic Banach space of distribution similar to the one used before by Demers & Liverani and by Liverani & Terhesiu.