There are several ways to consolidate IRA accounts. Rollovers, allowed once per year, entail taking receipt of the funds and transferring them to another institution within 60 days. This method of consolidation generates a notice to the IRS, so be sure you keep your paperwork in order; you'll need it if questioned.
With a direct transfer from one custodian to another, assets never touch human hands (at least not yours), and the IRS doesn't usually receive a notice. Make your life easier, and let your new custodian's fingers do the walking.