Transitive group action

A group action is transitive if for each $a,b\in X$ there exists $g\in G$ such that $b=a\cdot g$. I think that it is called locally transitive if $X$ is a manifold and for every $p\in X$ we can find an open neighbourhood $U$ such that the restricted action is transitive. I suppose that in this case we have to speak of local group of transformations.