It's not too too hard to compute homology of a chain complex whose differentials are all zero. In this talk, based on joint work with Nathan Kershaw, we propose a new perspective on the persistence pairing algorithm, suggesting that it replaces a filtration of chain complexes over a field by a quasi-isomorphic one with zero differentials. This perspective recovers the standard persistence pairing algorithm with compression and retrospective reduction of Bauer, Bin Masood, Giunti, Houry, Kerber, and Rathod from “Keeping it sparse: Computing persistent homology revisited." It further permits one additional improvement that, when implemented, outperforms Ripser in dimension 1 in most of the cases we tested.