Mavericks unstable on macbook pro

Unstable in what way?

If it's a 15-inch 2010 MBP, see below.

You have the MacBookPro6,2, the Edsel of Macs. It may have a logic board defect covered by this recall.

Make a "Genius" appointment at an Apple Store, or go to another authorized service provider, to have the machine tested. The routine hardware diagnostics used by service providers do not detect the fault. There is a specific test for this issue.

Print the first page of the panic report, and the support page linked above, and bring them with you.

Note that the recall only applies within three years of purchase. After that, Apple may refuse the service. In that case, you may be quoted a price of about $300 (in the U.S.) for a "depot repair," which involves shipping the unit to a central repair facility and takes about two weeks. For that flat fee, anything found wrong with it should be fixed, not just the logic board.

The model was discontinued in February 2011, so the replacement program will be ending soon. Some units may have been sold by Apple as refurbished after that date.

Back up all data on the internal drive(s) before you hand over your computer to anyone. If privacy is a concern, erase the data partition(s) with the option to write zeros* (do this only if you have at least two complete, independent backups, and you know how to restore to an empty drive from any of them.) Don’t erase the recovery partition, if present.

*An SSD doesn't need to be zeroed.

Sometimes persuasiveness helps. Good luck.