Within a region, Anycast is how many big companies move things around mostly seamlessly. Why inside a region? If RIPE or ARIN catch you advertising their IP in the other's territory, they will send nasty emails and threaten to take back your CIDR blocks. I have no idea if they will follow through as we always stopped violating their rules when told to.

Outside of a region, they use DNS and sometimes a combination of WAN accelerators and VPN's, dark fiber.