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For projective conifold transitions between Calabi-Yau threefolds $X$ and$Y$, with $X$ close to $Y$ in the moduli, we show that the combined informationprovided by the $A$ model (Gromov--Witten theory in all genera) and $B$ model(variation of Hodge structures) on $X$, linked along the vanishing cycles,determines the corresponding combined information on $Y$. Similar result holdsin the reverse direction when linked with the exceptional curves.

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