Let us consider the Whitney sum $E$ of holomorphic line bundles $L_1,\dots, L_k$ on a smooth (projective) variety $X$. For a generic global section $s$ of $E$, the zero locus $Z_s := s^{-1}(0_E)$ forms a (smooth) subvariety of $X$.
I would like to know how "similar" the subvarieties $X_s$ and $X_t$ for different generic sections $s$ and $t$ are.
I think that they are connected by a deformation family (i.e. we have a smooth proper map $f:Y \to B$ with connected $B$ such that $X_s \simeq f^{-1}(b)$ and $X_t \simeq f^{-1}(b')$), because some papers say so an implicit way. But I can not find any relevant information about my question in books/lecture notes on deformation theory.
Can you tell me any relevant resources mentioning a precise statement about my question?