  We describe deformations of the noncompact Calabi-Yau threefolds $W_k =
\mbox{Tot}(\mathcal{O}_{\mathbb{P}^1}(-k) \oplus
\mathcal{O}_{\mathbb{P}^1}(k-2))$ for $k=1,2,3$, as well as their moduli of
holomorphic vector bundles of rank $2$. Deformations are computed concretely by
calculations of $H^1(W_k, TW_k)$. Information about the moduli of vector
bundles is obtained by analysing bundles that are extensions of line bundles.
We show that for each $k=1,2,3$ the associated structures are qualitatively
different, and we also comment on their difference from the analogous
structures for the simpler noncompact twofolds
$\mbox{Tot}(\mathcal{O}_{\mathbb{P}^1}(-k))$ which had been studied previously
by the authors.
  We describe deformations of the noncompact Calabi-Yau threefolds $W_k =
\textrm{Tot}(\mathcal{O}_{\mathbb{P}^1}(-k) \oplus
\mathcal{O}_{\mathbb{P}^1}(k-2))$ for $k=1,2,3$. We compute deformations
concretely by calculations of $\textrm{H}^1(W_k, TW_k)$ via \v{C}ech
cohomology. We show that for each $k=1,2,3$ the associated structures are
qualitatively different, and we also comment on their difference from the
analogous structures of simpler noncompact twofolds
$\textrm{Tot}(\mathcal{O}_{\mathbb{P}^1}(-k))$.
