Calibre is an awesome little program ... but it won't help here. You have run into the DRM problem, where each bookstore's books won't run on another (as a general rule).
To be able to open a book in an ereader different from the one controlled by the store from where you've bought the books, you'll have to remove the DRM. Note that this also includes the Kindle.
There is plenty of data available on the web to help you remove DRM. Just know that in some countries, removing DRM is considered illegal. Oh, and no one has [yet] figured out how to remove the DRM that comes with ebooks you buy from the Apple store for the iBooks app.
A further plug for Calibre: If you have ebooks unencumbered with DRM, you can use it to manage your book files, convert to a format for reading on whichever device you wish, etc. Yes, you can use Calibre to manage your DRM'd ebooks - you just can't do as much with them (such as convert them to a different format). But, I'd highly recommend Calibre for anyone with an ebook library. The program is a free download. Just, please, give a donation to the creator, Kovid, as he works full-time on this most awesome program (and help him be able to continue improving/working on Calibre).
Marilyn