# Degeneration of cycle class map

Let $$f:\mathcal{X} \to \Delta$$ be a flat family of projective varieties, smooth over the punctured disc $$\Delta^*$$ and the central fiber is a simple normal crossings divisor. Let $$\mathcal{Z} \subset \mathcal{X}$$ be a closed subscheme of relative codimension, say $$p$$, and flat over $$\Delta$$. Does the central fiber $$\mathcal{Z}_0$$ of $$\mathcal{Z}$$ define an element, say $$\eta$$ in $$H^{2p}(\mathcal{X}_0,\mathbb{C})$$ such that under the specialization morphism $$H^{2p}(\mathcal{X}_0,\mathbb{C}) \to H^{2p}(\mathcal{X}_t,\mathbb{C})$$ for $$t \in \Delta^*$$ general, $$\eta$$ maps to the cohomology class of $$[\mathcal{Z}_t] \in H^{2p}(\mathcal{X}_t,\mathbb{C})$$? Any reference will be most welcome.