In the context of the question, the 10-dimensional spacetime is $\mathbb{R}^{1,3} \times X$ where $X$ is a Calabi-Yau 3-fold. Considering type IIB string theory on this geometry, without branes and with no fluxes turned on, gives rise to an effective theory on $\mathbb{R}^{1,3}$ with $\mathcal{N}=2$ supersymmetry. If one wants to go from $\mathcal{N}=2$ to $\mathcal{N}=1$ supersymmetry on $\mathbb{R}^{1,3}$, one can try to add D-branes. If one wants to preserve Poincaré invariance of $\mathbb{R}^{1,3}$, the D-brane has to fill in entirely $\mathbb{R}^{1,3}$ (it is interesting to consider cases where one does not preserve Poincaré invariance of $\mathbb{R}^{1,3}$ but I don't think that it is the context of the question). So the only possibilities, given that $Dp$-branes in IIB string theory have $p$ odd, are $D3$-branes wrapping 0-cycles in $X$, $D5$-branes wrapping 2-cycles in $X$ and $D7$-branes wrapping 4-cycles in $X$. In particular, there is nothing to wrap around a non-trivial 3-cycle.

Starting with $D5$-branes wrapping some non-trivial 2-cycle $S^2$ in $X$ and realizing the geometric transition consisting in shrinking $S^2$ and growing up some $S^3$, one can ask what happens to the theory: the $D5$ branes disappear, so how is it possible to still have $\mathcal{N}=1$ (and not $\mathcal{N}=2$)? The answer is that now there is a non-zero flux through $S^3$ (it is a field strength flux for the 2-form gauge field present in the Ramond-Ramond sector of IIB. Remark that the $D5$-branes are magnetic sources for this 2-form gauge field and the idea is that during the geometric transition, the $D5$-branes disappear but the corresponding magnetic field remains).