  We prove a sort of reconstruction theorem for generic elliptic Calabi-Yau
$3$-folds in the sense of C\u{a}ld\u{a}raru. From our argument it follows that
two generic elliptic Calabi-Yau $3$-folds are derived-equivalent linear over
the base if and only if their generic fibers are derived-equivalent. As an
application, we give affirmative answers to the conjectures raised by
Knapp-Scheidegger-Schimannek. Namely, for each pair of elliptic Calabi-Yau
$3$-folds in their list we prove that they share the relative Jacobian and are
$P^2$-linear derived-equivalent.
