  We show a general relation between fixed point stability of suitably
perturbed transfer operators and convergence to equilibrium (a notion which is
strictly related to decay of correlations). We apply this relation to
deterministic perturbations of a large class of maps with indifferent fixed
points. It turns out that the $L^1$ dependence of the a.c.i.m. on small
suitable deterministic changes for these kind of maps is H\"older, with an
exponent which is explicitly estimated.
