Resistor in between two meshes
There's no current flowing because there's no loop. Current has to flow in a closed loop, so no current can flow through that resistor.

The voltage being the same on both sides is because of ohm's law; with no current through a resistor, both sides must be at the same voltage. You'll notice that, to make this work, the negative terminal of the left voltage source is now at -1.33 V relative to ground.