When I moved to CO, I brought lots of already-bottled beer with me, and the elevation gain was almost 9,000 feet. No problems yet, although some of the beers with higher carbonation foam over when opened.
The pressure difference in going from sea level to 6,000 ft is only about 2 psi. For the area of the bottle neck, you could pull on the top with more force.
Edit: Totally unrelated, but when I went home for the holidays this year I traveled with 29 beers in my checked bag. TSA really seemed to enjoy searching it and running every single bottle/can through the scanner... my Xmas gift to them.