2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69410We derive general Novikov-Morse type inequalities in a Conley type framework for flows carrying cocycles, therefore generalizing our results in [FJ2] derived for integral cocycle. The condition of carrying a cocycle expresses the nontriviality of integrals of that cocycle on flow lines. Gradient-like flows are distinguished from general flows carrying a cocycle by boundedness conditions on these integrals.35pages, 6 figuresGeometric Topology37B30,37B35,57R70text