I'll describe new bigraded invariants of a framed link in a 3-manifold, which arise as the pages of a spectral sequence generalizing the surgery exact triangle in monopole Floer homology. The construction relates the topology of link surgeries to the combinatorics of polytopes called graph associahedra. For a link in the 3-sphere, we obtain a sequence of bigraded vector spaces, interpolating between the reduced, $Z/2Z$ Khovanov homology and a version of the monopole Floer homology of the branched double cover. This perspective also yields a simple, topological proof that odd Khovanov homology is mutation invariant.Paper references: http://arxiv.org/abs/0903.3746, http://arxiv.org/abs/0909.0816