  Previously we constructed Calabi-Yau threefolds by a differential-geometric
gluing method using Fano threefolds with their smooth anticanonical $K3$
divisors in arXiv:1305.0074. In this article we further consider the
diffeomorphic types of the resulting Calabi-Yau threefolds starting from
different pairs of Fano threefolds of Picard number one.
