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.