Real plane sextics without real points

We prove that the equisingular deformation type of a simple real plane sextic curve with smooth real part is determined by its real homological type, , the polarization, exceptional divisors, and real structure recorded in the homology of the covering $K3$-surface. As an illustration, we obtain an equisingular deformation classification of real plane sextics with empty real part (for completeness, we consider the few non-simple ones as well).