  We introduce a new continuity method which provides an alternative way of
carrying out the Analytic Minimal Model Program introduced by G. Tian and J.
Song and G. Tian. This equation -- unlike the Ricci flow -- has the advantage
of having Ricci curvature bounded from below along the deformation, so that the
compactness theory of Cheeger-Colding-Tian for Kaehler manifolds and the
partial $C^0$-estimate, can be applied.
