Alpha / Beta Testing on Google PlayStore

I have an open beta test and a closed alpha test for my current android app.
The URLs for both are the same and I cannot change them.(?)

I need to get a smartphone in the alpha test, but after adding the mail address to the closed alpha test group in the DevConsole and submitting to the group (I don't know which, there is no hint) on the smartphone via the URL, it seems that I just entered the open beta test group.

How can I be sure in which test group (alpha / beta) I am?
Can I change between the two states?
Can I change the submit-URL?