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Poincaré series of p-adic, definable equivalence relations have been studied in various cases since Igusa's and Denef's work related to counting solutions of polynomial equations modulo p n for prime p. General semi-algebraic equivalence relations on local fields have been studied uniformly in p recently by Hrushovski, Martin and Rideau (2014). In this paper we generalize their rationality result to the analytic case, uniformly in p, we build further on their appendix given by Cluckers as welldoi:10.1090/btran/23 fatcat:zwebttsokzb7dgevmdgj3lr6bi