In E, the minor blues scale notes are E, G, A, Bb, B, D. In A, the minor blues scale notes are A, C, D, Eb, E, G. In B, the minor blues scale notes are B, D, E, F, F#, A.
You can see there are some common notes - A, D and E being them.Theoretically, if you only played these, they would work over all 3 chords. But the tune may start to get boring! Not all notes played over a chord HAVE to fit the chord, but the best one ought to be the one with the same name - the root, often played on beat 1. One on one, I call it. Other notes are usable, so you could just use the original minor blues notes all through, even over A7 and B7. Most will fit, and not sound too bad, especially if you phrase it right. However, using the better fitting notes as mentioned earlier, a better fit will be heard. I.e. the A notes fit A better than, say, the E.
There is the same idea available using the major blues notes. A lot of blues players will move between the two lots, but also tend to use the minor blues mostly, bending the G to G# on the E for instance, or even just tweaking it so it sounds like it was a G#, but actually only went half way there.
So, in summary - stick to the E notes all through, with careful omissions and timing, or, when you are feeling brave (adventurous !) change the set of notes to match the appropriate chord.
Cream's Sunshine of your Love shows this well, in that the riff changes when the chord underneath changes. Just like so many blues and pop numbers do.