  A version of Kirby calculus for spin and framed three-manifolds is given and
is used to construct invariants of spin and framed three-manifolds in two
situations. The first is ribbon *-categories which possess odd degenerate
objects. This case includes the quantum group situations corresponding to the
half-integer level Chern-Simons theories conjectured to give spin TQFTs by
Dijkgraaf and Witten \cite{DW90}. In particular, the spin invariants
constructed by Kirby and Melvin \cite{KM91} are shown to be identical to the
invariants associated to $\mathrm{SO}(3).$ Second, an invariant of spin
manifolds analogous to the Hennings invariant is constructed beginning with an
arbitrary factorizable, unimodular quasitriangular Hopf algebra. In particular
a framed manifold invariant is associated to every finite-dimensional Hopf
algebra via its quantum double, and is conjectured to be identical to
Kuperberg's noninvolutory invariant of framed manifolds associated to that Hopf
algebra.
