  The problem of prescribing conformally the scalar curvature of a closed
Riemannian manifold as a given Morse function reduces to solving an elliptic
partial differential equation with critical Sobolev exponent. Two ways of
attacking this problem consist in subcritical approximations or negative pseudo
gradient flows. We show under a mild none degeneracy assumption the equivalence
of both approaches with respect to zero weak limits, in particular an one to
one correspondence of zero weak limit finite energy subcritical blow-up
solutions, zero weak limit critical points at infinity of negative type and
sets of critical points with negative Laplacian of the function to be
prescribed.
