  We provide an explicit twistorial construction of quaternion-Kahler manifolds
obtained by deformation of c-map spaces and carrying an isometric action of the
modular group SL(2,Z). The deformation is not assumed to preserve any
continuous isometry and therefore this construction presents a general
framework for describing NS5-brane instanton effects in string
compactifications with N=2 supersymmetry. In this context the modular invariant
parametrization of twistor lines found in this work yields the complete
non-perturbative mirror map between type IIA and type IIB physical fields.
