As I understand it (and I could well be talking out of my fundament)...
If you’re going up to the fifth you’ll be playing the major 3rd, 4th, flat 5th (the “blue note”) and 5th which will work nicely in a rock blues setting so long as the flat fifth is just a passing tone.
If you’re going to the root you’re playing the 6th, flat 7, major 7 and root. Again, that flat 7/major 7 in a rock/blues context works nicely as passing tones before resolving to the root.
In both cases, you’re introducing a note that clashes slightly before resolving it on the fifth or the root.
Theres probably a better explanation but that’s how I’ve explained it to myself....