Spectral-sequence conjecture for RG flows from 4d N=4 theory

Let a 4d $\mathcal{N}=2$ theory be reachable from 4d $\mathcal{N}=4$ super-Yang–Mills theory by an RG flow, and let $M_3$ be a 3-manifold. Spectral-sequence conjecture. The RG flow induces a spectral sequence whose starting page is $\mathcal{H}_{\mathrm{VW}}(M_3)$ and which converges to Floer-like homology in the resulting $\mathcal{N}=2$ theory. The claim is motivated by relevant deformations preserving at least $\mathcal{N}=2$ supersymmetry; the source does not establish it or specify further conditions ensuring such a spectral sequence.