Welcome to Apple Support Communities.
It sounds like you're seeing an issue with purchases not downloading in iTunes on your MacBook Air. The article linked below provides tips that should resolve the issue for you.
If your download was interrupted using your Mac or PC
- Open iTunes.
- Choose Store > Check for Available Downloads.
- Type your account name and password if prompted.
If these steps didn't work for you, try the following steps to resolve issue.
- Restart your iOS device or computer.
- Check for updates for your Mac or PC and install any software updates. Also, update any security software you may have (anti-virus, anti-malware, firewall, and so on).
- If using Wi-Fi for Internet access, try using a different Wi-Fi network when downloading. If you are connecting to a home network, try restarting your Wi-Fi router. Also, check for and install any firmware updates for your Wi-Fi router. (Refer to the manufacturer's website for your router to get information on updating its firmware.)
- If you are using a Mac or PC, try using an Ethernet cable for wired Internet access instead of using Wi-Fi. If the issue is still unresolved and you're using iTunes for Windows, follow the steps to troubleshoot security software issues.
I hope this helps.