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.
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Author of the notes: Antonio J. Pan-Collantes
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