  For every rational homology 3-sphere with 2-torsion only we construct a
unified invariant (which takes values in a certain cyclotomic completion of a
polynomial ring), such that the evaluation of this invariant at any odd root of
unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root and
at any even root of unity the SU(2) quantum invariant. Moreover, this unified
invariant splits into a sum of the refined unified invariants dominating spin
and cohomological refinements of quantum SU(2) invariants. New results on the
Ohtsuki series and the integrality of quantum invariants are the main
applications of our construction.
