Instanton Bundles on the Blowup of the Projective 3-Space at a Point

We propose a general definition of mathematical instanton bundle with given charge on any Fano threefold extending the classical definitions on P-3 and on Fano threefold with cyclic Picard group. Then we deal with the case of the blowup of P-3 at a point, giving an explicit construction of instanton bundles satisfying some important extra properties. Moreover, we show that they correspond to smooth points of a component of the moduli space.