The explanation about there being no Potential difference between Earth and neutral is correct, however in seeing bot cycles when you monitor the LINE or Live wire you may understand it better by thinking about what is actually happening in the conductor.
The Electrons that are moving flow at approximately 27 cm an hour in copper (thats just over an inch in US terms), so at 50 or 60 Hz the time they have to move is only around 20ms so they don't move far !! They are in fact only being shuffled back and forth over about 150um.
The electrons in BOTH conductors will be doing the same. The Negative cycle you are talking about is merely indicating a change of direction of the current. When the flow stops at the zero crossing point of the sine wave there os no Potential difference anywhere, but it will increase to maximum at the peak no matter what direction the current is flowing in.
Thats a lot to take in but hope it helps.