  It is known that there is a bijection between the perturbed closed geodesics,
below a given energy level, on the moduli space of flat connections M and
families of perturbed Yang-Mills connections depending on a small parameter. In
this paper we study the heat flow on the loop space on M and the Yang-Mills
L^2-flows for a 3-manifold N with partial rescaled metrics. Our main result is
that the bounded Morse homology of the loop space on M is isomorphic to the
bounded Morse homologies of the connections space of N.
