You can get to Pyatigorsk either by air, rail or bus from Moscow or Simferopol.

This is not quite true. You can't fly directly to Pyatigorsk. You CAN take a train directly there but it's a long trip (at least 8 hours and very likely much more) no matter where you're coming from.You can fly to Min. Vody directly from Moscow, Sochi, Rostov, or St. Petersburg, and Min. Vody is about a 25 minute drive from pyatigorsk, or an hour bus ride (so many stops...)