On the connectedness of the standard web of Calabi-Yau 3-folds and small transitions

We supply a detailed proof of the result by P.S. Green and T. H$\ddot{\text{u}}$bsch that all complete intersection Calabi–Yau 3-folds in product of projective spaces are connected through projective conifold transitions (known as the standard web). We also introduce a subclass of small transitions which we call primitive small transitions and study such subclass. More precisely, given a small projective resolution $\pi : \widehat{X} \rightarrow X$ofaCalabi--Yau3-fold$X$, we show that if the natural closed immersion $Def(\widehat{X})\hookrightarrow Def(X)$ is an isomorphism then $X$ has only ODPs as singularities.