In one of my particle physics textbooks, I came across the statement that U(1) and SO(2) are locally equivalent. I don’t really know what it means. I know a bit of group theory and that $U(1)$ is just the group of $1$-D unitary transformations and $SO(2)$ the $2$-D proper rotation group.
Could anyone explain the statement in both a formal and intuitive way? Thanks!