A spanning tree cohomology theory for links

In their recent preprint, Baldwin, Ozsváth and Szabó defined a twisted version (with coefficients in a Novikov ring) of a spectral sequence, previously defined by Ozsváth and Szabó, from Khovanov homology to Heegaard–Floer homology of the branched double cover along a link. In their preprint, they give a combinatorial interpretation of the E3E3-term of their spectral sequence. The main purpose of the present paper is to prove directly that this E3E3-term is a link invariant. We also give some concrete examples of computation of the invariant.