  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.
