Instanton bundles on two Fano threefolds of index $1$

We deal with instanton bundles on the product ${\mathbb P}^1\times{\mathbb P}^2$andtheblowupof${\mathbb P}^3$ along a line. We give an explicit construction leading to instanton bundles. Moreover, we also show that they correspond to smooth points of a unique irreducible component of their moduli space.