Trouble reinstalling OS after wipe of Mac Air

Repair a storage device in Disk Utility on Mac

Disk Utility can fix certain disk problems—for example, multiple apps quit unexpectedly, a file is corrupted, an external device doesn’t work properly, or your computer won’t start up. Disk Utility can’t detect or repair all problems that a disk may have.

If you run First Aid on a disk, Disk Utility checks the partition maps on the disk and performs some additional checks, and then checks each volume. If you run First Aid on a volume, Disk Utility verifies all the contents of that volume only.

1. In the Disk Utility app  on your Mac, choose View > Show All Devices.
2. Note: If you’re checking your startup disk or startup volume, restart your computer in macOS Recovery, select Disk Utility in the macOS Utilities window, then click Continue. If you check your startup volume (Macintosh HD), make sure you also check your data volume (Macintosh HD - Data).
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4. In the sidebar, select a disk or volume, then click the First Aid button .
5. If Disk Utility tells you the disk is about to fail, back up your data and replace the disk—you can’t repair it. Otherwise, continue to the next step.
6. Click Run, then click Continue.
7. If Disk Utility reports that the disk appears to be OK or has been repaired, you’re done. You can click Show Details to see more information about the repairs. Otherwise, you may need to do one of the following.

• • If Disk Utility reports “overlapped extent allocation” errors, two or more files occupy the same space on your disk, and at least one of them is likely to be corrupted. You need to check each file in the list of affected files. Most of the files in the list have aliases in a DamagedFiles folder at the top level of your disk.
    • If you can replace a file or re-create it, delete it.
    • If it contains information you need, open it and examine its data to make sure it hasn’t been corrupted.
  • If Disk Utility can’t repair your disk, or you receive a report that the First Aid process failed, try to repair the disk or partition again. If that doesn’t work, back up as much of your data as possible, reformat the disk, reinstall macOS, then restore your backed-up data.

If your Mac has a Fusion Drive and you see a flashing question mark or alert, see the troubleshooting section of the Apple Support article About Fusion Drive, a storage option for some Mac computers.

If you continue to have problems with your disk or it can’t be repaired, it may be physically damaged and need to be replaced. For information about servicing your Mac, see Find out how to service or repair your Mac.

1. Start up from macOS Recovery

To start up from macOS Recovery, turn on your Mac and immediately press and hold one of the following combinations on your keyboard. Command-R is generally recommended, especially if you never installed macOS Sierra 10.12.4 or later… https://support.apple.com/en-us/HT204904#notupdated

Command (⌘)-R

Install the latest macOS that was installed on your Mac.

Option-⌘-R

Upgrade to the latest macOS compatible with your Mac.

Shift-Option-⌘-R

Install the macOS that came with your Mac, or the closest version still available.

2. Decide whether to erase (format) your disk

If you need to erase your disk before installing macOS, select Disk Utility from the Utilities window, then click Continue. You probably don't need to erase, unless you're selling or giving away your Mac or have an issue that requires you to erase. Learn more about when and how to erase.

3. Install macOS

After starting up from macOS Recovery, follow these steps to install macOS:

1. Choose Reinstall macOS (or Reinstall OS X) from the Utilities window.
2. Click Continue, then follow the onscreen instructions to choose your disk and begin installation.
3. If the installer asks to unlock your disk, enter the password you use to log in to your Mac. If it doesn't see your disk, or it says that it can't install on your computer or volume, you might need to erase your disk. 

1. Please allow installation to complete without putting your Mac to sleep or closing its lid. During installation, your Mac might restart and show a progress bar several times, and the screen might be empty for minutes at a time.

If your Mac restarts to a setup assistant, but you're selling or giving it away, press Command-Q to quit the assistant without completing setup. Then click Shut Down. When the new owner starts up the Mac, they can use their own information to complete setup.

If you never installed macOS Sierra 10.12.4

If macOS Sierra 10.12.4 or later was never installed on your Mac, macOS Recovery works differently:

• Command-R is still the recommended way to start up from macOS Recovery. This combination makes sure that the installation isn't associated with your Apple ID, which is important if you're selling or giving away your Mac.
• Option-Command-R installs the macOS that came with your Mac, or the closest version still available.
• Shift-Option-Command-R isn't available.

https://support.apple.com/en-us/HT204904