Even if you ARE on Edge you can keep your device IF you pay all 20 or 24 payments as set by your Edge agreement.
"To be eligible to Edge Up, your original Edge device must be returned in good working condition and have no significant damage as determined by Verizon Wireless. Note to customers with Edge agreements signed prior to 6/1/14: You'll keep your 24-month Edge agreement, and will have the option to Edge Up to a new device after paying 75% of the original device, and returning the original device to us in good working condition"
This is copy from Verizon web,I don't see anything saying that you can keep your old device.
It would help if Verizon hadn't given it nonsensical terms... Early Edge, Edge, Edge Up...
Edge Up, mean upgrading before you have completed paying for a device. Which can be done in as little as 30 days if you pay the minimum required ( 50 or 75% )
once you pay 100% of the Edge installment plan, the phone is yours to keep.