The answer to your question is 3, based on his transaction history (2 done by a user, 1 done by simmy, noted in red text).
If they have between 3 and 6 years of Major League service, they can go to arbitration.
Of course you have option years, 6-year minor league free agency, and the Rule 5 draft to limit how much you can screw with them before you lose them.
So Martin has 3 years of ML service time, but he's also out of options. So if you leave him in the minors off the 40-man, he becomes a minor league free agent. If you call him up, he would have to clear waivers before being sent back down.