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Let $B$ be a smooth projective surface, and $\mathcal{L}$ an ample linebundle on $B$. The aim of this parer is to study the families of ellipticCalabi--Yau threefolds sitting in the bundle $\mathbb{P}(\mathcal{L}^a \oplus\mathcal{L}^b \oplus \mathcal{O}_B)$ as anticanonical divisors. We will showthat the number of such families is finite.

Families of Calabi-Yau elliptic fibrations in $\mathbb{P}(\mathcal{L}^a \oplus \mathcal{L}^b \oplus \mathcal{O}_B)$