Software for offline backup
 

I need make a backup from a disk in my home to a disk in my work.
Using rsync and internet is not possible, files are too big.
Changes are always made on my home and need sincronize with an external hdd these changes (files/folder new,modifications,deletion) and in work, apply that changes.

For example, now data in home and in work are the same.
I modify, add or delete a file in home, then sync with external hdd, external hdd doesn't have the data, only a list of files in work and his last modification date for compare, so, the sync must copy the new/modified file or the information that the file has been deleted. Then in work sync hdd with the internal disk and copy that file modified/new or delete file that was deleted in home.
Same for folders.
No need for backup older files.

Those scripts do something like that, but not propagate files/folders deletion
https://www.thanassis.space/Offline-rsync.html

Is it really a backup software you're asking for? From your explanation I understood that what you really want is to keep your home and work data in sync and not backing up any of them. If so, I would use git. If you create a bare repository on your external hdd (not a working copy) it wouldn't contain the data itself, only the metadata.