When you merge tickets, you are asked which ticket number you want to keep. The one you don't keep gets closed and a history entry is created on the closed ticket: "Merged with Ticket ##### and set Status Type to Closed." The client of the original ticket is not notified.
Generally when you have duplicate tickets, they are from or about the same client (maybe Sue and Sue's assistant both reported Sue's printing problem--you can keep Sue's ticket and merge Sue's assistant's ticket--Sue's assistant won't be notified, but that's probably ok...you can CC her if you need to).
If they are from different clients, then you have a "problem" with multiple "incidents". For example, both Sue and John cannot print because the Floor 4 Copy Room printer is broken and needs repair, and they have both submitted tickets to that effect. In this case, what I do is create a new ticket with ticket type "Problem" about the Floor 4 Copy Room printer being broken and needing repair. Then I change the tickets from Sue and John to the "incident" ticket type and link them both to the "Problem" ticket (use the Problems tab out to the side of the Ticket Details screen on each individual ticket/incident).
Thanks. That was what I was looking for.