Hi there, shiromiwijet2003!
Thanks for reaching out to the Apple Support Communities! It sounds like you're having an issue upgrading from Mavericks to Catalina on your MacBook Air. I recommend taking a look at this article with steps to follow for How to use safe mode on your Mac. This will perform checks and stop certain software from starting up automatically. Once you are in safe mode, test to see if you have the same issue upgrading.
I also suggest going to the Applications folder and deleting the installer for macOS Catalina. Then, try and download it again and see if you are able to install it.
If you still have an issue completing the upgrade, check out this article if you haven't already for How to back up your Mac to be sure you have backed up any important personal information on the Mac. Once you have a back up, check out this article for How to reinstall macOS from macOS Recovery and reboot your MacBook Air into macOS Recovery using Option-Command-R keys. Once there, see if you can upgrade the macOS to the latest version available.
Let me know the results and have a great day!