  In their recent preprint, Baldwin, Ozsv\'{a}th and Szab\'{o} defined a
twisted version (with coefficients in a Novikov ring) of a spectral sequence,
previously defined by Ozsv\'{a}th and Szab\'{o}, 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 $E_3$-term of their
spectral sequence. The main purpose of the present paper is to prove directly
that this $E_3$-term is a link invariant. We also give some concrete examples
of computation of this invariant.
