  We generalize the formula of Gromov-Witten-Welschinger invariants of
$\mathbb{C} P^3$ established by E. Brugall\'e and P. Georgieva in [BG16b] to
$\mathbb{C} P^3\#\overline{\mathbb{C} P}^3$. Using pencils of quadrics, some
real and complex enumerative invariants of $\mathbb{C}
P^3\#\overline{\mathbb{C} P}^3$ can be written as the combination of the
enumerative invariants of the blow up of $\mathbb{C} P^2$ at two real points.
