*S*^3, and it was extended for links in I-bundles over surface by Asaeda, Przytycki and Sikora. In this talk, we will exhibit some generalization of their construction for null homologous links in ℝℙ3. On the other side of the story, Ozsvath and Szabo defined a spectral sequence relating the Heegaard Floer homology of the branched double cover of *S*^3 over *L* to the Khovanov homology of *L*. We will extend this construction for null homologous links in ℝℙ3 as well, relating the Heegaard Floer homology of the branched double cover of ℝℙ3 over *L* to our Khovanov-type homology of *L*.