Connectedness conjecture for the graph of simply connected Calabi–Yau threefolds

Consider the graph whose nodes are deformation classes of simply connected Calabi–Yau threefolds and whose edges are given by geometric transitions. Call a node primitive if its deformation class contains no Calabi–Yau threefold admitting a birational contraction to a projective normal threefold. Connectedness conjecture. The graph of simply connected Calabi–Yau threefolds is connected. Their moduli can then be described by starting from the primitive nodes, which in general are given by deformation classes of Calabi–Yau threefolds with Picard number $1$. This conjecture proposes a connected geometric-transition network for simply connected Calabi–Yau threefolds; the supplied passage gives no resolution.