  We argue that the complete Klebanov-Witten flow solution must be described by
a Calabi-Yau metric on the conifold, interpolating between the orbifold at
infinity and the cone over T^(1,1) in the interior. We show that the complete
flow solution is characterized completely by a single, simple, quasi-linear,
second order PDE, or "master equation," in two variables. We show that the
Pilch-Warner flow solution is almost Calabi-Yau: It has a complex structure, a
hermitian metric, and a holomorphic (3,0)-form that is a square root of the
volume form. It is, however, not Kahler. We discuss the relationship between
the master equation derived here for Calabi-Yau geometries and such equations
encountered elsewhere and that govern supersymmetric backgrounds with multiple,
independent fluxes.
