Updating to macOS Catalina gets stuck, when trying to update from OS X Mavericks
The jump from Mavericks to Catalina may be too much of a leap. Try first upgrading to High Sierra. The website How to upgrade to macOS High Sierra has a link you can use to download the High Sierra upgrade. I suggest this because the installation of High Sierra will also upgrade the firmware to recognize and boot from APFS containers. While this is not a requirement for High Sierra, it is for Catalina.