A + B theory in conifold transitions for Calabi-Yau threefolds

For projective conifold transitions between Calabi-Yau threefolds $X$ and $Y$, with $X$ close to $Y$ in the moduli, we show that the combined information provided by the $A$ model (Gromov--Witten theory in all genera) and $B$ model (variation of Hodge structures) on $X$ determines the corresponding combined information on $Y$, and vice versa.