This is not merging.
Merging tickets has been requested before, but this request is for parent problem tickets and child incidents.
Merging tickets makes sense for things like when the same user keeps sending a new e-mail instead of replying to you.
Parent/Child ticket relationships are good for when multiple people report the same incident.
These tickets should not be merged and treated as the same ticket.
Instead these tickets should be attached to a master/parent problem ticket.
The parent ticket describes the underlying problem and when closed would in turn close the incident tickets.