Using ABS or PVC cement, select a well ventilated work area and read all safety precautions and directions before proceeding.
If your choice of cement came with a dabber affixed to the inside of the lid, apply lightly to both the outer rim of the PVC tube area you've sanded, as well as to the inner neck of the cut bottle top.
Depending on your cement, and amount applied, it may dry quickly, so just work on one bottle top / PVC combination at a time.
Once both parts have cement applied, fit them together and apply some pressure while rotating approximately a quarter of a turn.
This will help both parts to bond better.
Once satisfied, repeat the process on the other bottle top / PVC set.
NOTE:   As a precaution, leave the screw on caps off their perspective bottle tops until the cement has dried and cured to avoid accidentally permanently affixing them to the bottle tops.  Cement should cure completely after several hours.