Node surgery principle for Calabi–Yau threefolds

Let $Y_t$ be a smooth fibre of a semistable degeneration with nodal central fibre $Y_0$, let $\beta\in H^{2,2}(Y_t,\mathbb{Q})$ be rational, and let $\delta_i\in H_3(Y_t,\mathbb{Z})$ be vanishing cycles associated with $k$ nodes. Assume that the pairings $\langle\beta,\delta_i\rangle$ generate the required algebraic components on a crepant resolution $\widetilde{Y}_0\to Y_0$. Node surgery principle. Then $\beta$ specializes to a combination of classes of exceptional divisors and their intersections in $H^4(\widetilde{Y}_0,\mathbb{Q})$, and is therefore algebraic in the limit. The principle is stated as a threefold analogue of the K3 node surgery construction; the supplied text gives no resolution status or further conditions guaranteeing the required generation.