I have been saving my old turbotax cds. will the newest edition open and work with earlier years such as 2020?

No each year is separate.   If you have a .tax file like .tax2020, .tax2021 etc you need that  year's program to open it.   You should be saving each  year as a pdf file so you don't need to open old returns or install old programs.    You might not be able to install older program.  And Turbo Tax only supports the last 3 years so you wouldn't be able to update older programs or download any state programs  you might need.  

OR you could try the TaxPrinter service to convert a .tax file to pdf at
https://www.taxprinter.com

What do you need to do with  the earlier years?    You only need the prior year tax file to Transfer into the next  year.  So you need the .tax2022 file to transfer into 2023.