When moving within the same datacenter, ie going from a VPS in TX to an SSD VPS in TX, we can do this behind the scenes with no service interruption. Unfortunately when changing geographical locations this isn't possible because an IP address can only be tied to a single network (read physical location), thus we have to assign new IPs.
Since existing functionality within the OS and control panels will fail to properly update IP addresses, we do require a new VPS to be purchased with new IPs at which point our support department will help you migrate your data over. Then the old VPS is cancelled.
Here's a step by step list on the proper procedure:
That's it, it's really that simple.