  We study general representations of the free group on two generators into
$SL(2,C)$, and the connection with generalized Markoff maps, following
Bowditch. We show that Bowditch's Q-conditions for generalized Markoff maps are
sufficient for the generalized McShane identity to hold for the corresponding
representations and that the subset of representations satisfying these
conditions is the largest open subset in the relative character variety on
which the mapping class group acts properly discontinuously. Moreover we
generalize Bowditch's results on variations of McShane's identity for complete,
finite volume hyperbolic 3-manifolds which fiber over the circle, with the
fiber a punctured-torus, to identities for incomplete hyperbolic structures on
such manifolds, hence obtaining identities for closed hyperbolic 3-manifolds
which are obtained by doing hyperbolic Dehn surgery on such manifolds.
