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. Hübsch 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 π: X → X of a Calabi-Yau 3-fold X, we show that if the natural closed immersion Def(X), [right arrow, hooked] Def(X) is an isomorphism then X has only ODPs as singularities.