Title: Alperin-McKay natural correspondences in solvable and symmetric groups for the prime $p=2$,
Abstract: Let $G$ be a finite solvable or symmetric group and let $B$ be a $2$-block of
$G$. We construct a canonical correspondence between the irreducible characters
of height zero in $B$ and those in its Brauer first main correspondent. For
symmetric groups our bijection is compatible with restriction of characters.