  We show the equivalence of the different types of pure spinor constraints
geometrically derived from the Free Differential Algebras of N=2 d=10
supergravities. Firstly, we compute the general solutions of these constraints,
using both a G_2 and an SO(8) covariant decomposition of the 10d chiral
spinors. Secondly, we verify that the number of independent degrees of freedom
is equal to that implied by the Poincare' pure spinor constraints so-far used
for superstrings, namely twenty two. Thirdly, we show the equivalence between
the FDA type IIA/B constraints among each other and with the Poincare' ones.
