In my talk I will first review the interpretation of the counts of
solutions of Kapustin-Witten equations on a 3-manifold times a line as
Stokes coefficients associated to the perturbative expansion of
Chern-Simons theory. These counts can be naturally combined into
q-series with integral coefficents, labelled by an ordered pair of flat
connections. I will then present an explicit algorithm/formula for
computing them for a large class of closed 3-manifolds. If time permits
I will also make some comments about categorification of these counts
and relation to Fukaya-Seidel category of connections on the 3-manifold.