EasyEDA support you save your file to local, you can download your design as EasyEDA source file.
You can create an EasyEDA source file via:
Document > EasyEDA Source…
Or Project > Right Click > Download Project, you will download a zip file with EasyEDA Source files for Schematics and PCBs.
EasyEDA Source is a JSON file which can be read by many other programs. Please see: