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A family of TQFTs parametrised by G-crossed braided spherical fusioncategories has been defined recently as a state sum model and as a Hamiltonianlattice model. Concrete calculations of the resulting manifold invariants arescarce because of the combinatorial complexity of triangulations, if nothingelse. Handle decompositions, and in particular Kirby diagrams are known tooffer an economic and intuitive description of 4-manifolds. We show that if3-handles are added to the picture, the state sum model can be convenientlyredefined by translating Kirby diagrams into the graphical calculus of aG-crossed braided spherical fusion category.  This reformulation is very efficient for explicit calculations, and themanifold invariant is calculated for several examples. It is also shown that inmost cases, the invariant is multiplicative under connected sum, which impliesthat it does not detect exotic smooth structures.

Evaluating TQFT invariants from G-crossed braided spherical fusion categories via Kirby diagrams with 3-handles