Rates of mixing for nonMarkov infinite measure semiflows

We develop an abstract framework for obtaining optimal rates of mixing and higher order asymptotics for infinite measure semiflows. Previously, such results were restricted to the situation where there is a first return Poincar\'e map that is uniformly expanding and Markov. As illustrations of the method, we consider semiflows over nonMarkov Pomeau-Manneville intermittent maps with infinite measure, and we also obtain mixing rates for semiflows over Collet-Eckmann maps with nonintegrable roof function.