  In this article we establish an explicit link between the classical theory of
deformations \`a la Gerstenhaber -- and a fortiori with the Hochschild
cohomology-- and (weak) PBW-deformations of homogeneous algebras. Our point of
view is of cohomological nature. As a consequence, we recover a theorem by R.
Berger and V. Ginzburg, which gives a precise condition for a filtered algebra
to satisfy the so-called PBW property, under certain assumptions.
