  We 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.
