No,' everyone' (and there are very few of these 'everyones') who runs three graphics cards is either using Crossfire with Radeon cards at x8, x4, x4, or is using a very expensive motherboard with a PLX chip at x16 x8 x8 and running Crossfire or SLI with NVidia.
Two 970s will run in SLI at x8 x8 on many boards in your budget. The Z97 chipset has insufficient PCIe lanes for x 16, x16. Even the new Skylake boards have insufficient lanes for x16, x16, x16.
As I said at the start, what you want is impossible for your budget, and I think it's a bad idea too. Thre-way anything, SLI or Crossfire is not worth it.