A bidirectional vertical arrow serving as both a delimiter and relation symbol for dual correspondences or vertical equivalences.
Examples
Showing bidirectional correspondence between sets
A \updownarrow B
Used as a delimiter for tall expressions
\left\updownarrow \begin{matrix} x + y \\ 2z \\ w - v \end{matrix}\right\updownarrow
Indicating two-way implication in logic
p \updownarrow q \text{ means } (p \rightarrow q) \land (q \rightarrow p)