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We study Kustin-Miller unprojections between Calabi-Yau threefolds or moreprecisely the geometric transitions they induce. We use them to connect manyfamilies of Calabi-Yau threefolds with Picard number one to the web of CalabiYau complete intersections. This enables us to find explicit description of afew known families of Calabi-Yau threefolds in terms of equations. Moreover wefind two new examples of Calabi-Yau threefolds with Picard group of rank one,described by Pfaffian equations in weighted projective spaces.

Geometric transitions between Calabi-Yau threefolds related to Kustin-Miller unprojections