We replace our earlier condition that physical states of the superstring
have non-negative grading by the requirement that they are analytic in a new real
commuting constant t which we associate with the central charge of the underlying
Kac-Moody superalgebra. The analogy with the twisted N=2 SYM theory suggests that
our covariant superstring is a twisted version of another formulation with an equivariant
cohomology. We prove that our vertex operators
correspond in one-to-one fashion to the vertex operators in Berkovits' approach
based on pure spinors. Also the zero-momentum cohomology is equal in both cases.
Finally, we apply the methods of equivariant cohomology to the
superstring, and obtain the same BRST charge as obtained earlier by relaxing the pure spinor
constraints.