Q: Can't download purchases to new MacBook air

Download past purchases

Downloading past purchases from the App Store, iBookstore, and iTunes Store

iTunes Store- Hiding and unhiding purchases

Authorization

iTunes Store- Authorize or deauthorize your Mac or PC.

In iTunes you use the Authorize This Computer or De-authorize This Computer option under the Store menu in iTunes' menubar. For Windows use the ALT-S keys to access it. Or turn on Windows 7 and 8 iTunes menus: iTunes- Turning on iTunes menus in Windows 8 and 7.