Spectral sequences in unoriented link Floer homology

In a previous work, we defined an unoriented skein exact triangle in unoriented link Floer homology. In this paper, we iterate a modified version of this exact triangle and obtain a spectral sequence from various versions of Khovanov homology to various versions of unoriented link Floer homology, over the field with two elements. In particular, for knots in $S^3$, we obtain a spectral sequence from the reduced Khovanov homology of the mirror of the knot to the knot Floer homology of the knot.