Three-manifold invariants $${\hat{Z}}$$ (“Z-hat”), also known as homological blocks, are q-series with integer coefficients. Explicit form for is SU(2) group, supergroup SU(2|1) and orthosymplectic OSp(2|2). We focus on SO(3) group OSp(1|2) in this paper. Particularly, the change of variable relating link to plays a crucial role explicitly writing q-series.
