Galois, normal, and regular covering spaces

Let \(p\colon\tilde X\to X\) be a covering space, let \(x_0\in X\), and let \(\Deck(\tilde X)\) be its group of deck transformations. The covering \(p\) is Galois, also called normal or regular, over \(x_0\) if \(\Deck(\tilde X)\) acts transitively on the fiber \(\inverseof{p}(x_0)\): for all \(\tilde x_1,\tilde x_2\in \inverseof{p}(x_0)\) there is \(\psi\in\Deck(\tilde X)\) with \(\psi(\tilde x_1)=\tilde x_2\).