The rational elliptic surface fibration deformation conjecture

Let $X$ be the rational elliptic surface and let $H=D_+\cup D_-$ be the union of two smooth fibers of its elliptic fibration. Rational elliptic surface deformation conjecture. The special Lagrangian fibration on $X\setminus\hat D$ should deform to a special Lagrangian family on $X\setminus H$ whose base $B$ is homeomorphic to a closed disc; over the interior, the fibers are special Lagrangian tori except for twelve nodal singular fibers, while over $\partial B$ the fibers are special Lagrangian annuli with one boundary component on each of $D_+$ and $D_-$. This is a more detailed specialization of the double-cover picture, and remains conjectural because the relevant deformation and boundary analysis are not established in general.