Book Crawler has file sharing enabled through iTunes so you can access your data files via USB. From iTunes, you would select your device after connecting, select the Apps tab, scroll to the bottom in the file sharing section and select bc. You should see files ending in "bcs" listed that you can save to your desktop. These bcs files represent the complete backup of your data which can also be used to transfer to a new device. If you are not new to Book Crawler, you may also see files ending in 'sqlite'. These are also database files which can be imported into bc and converted to the new 'bcs' format.
Older versions of BC defaulted to using "Crawler.sqlite" as the main database file. More recent versions now default to a file that starts with a timestamp and end in bcs (for example, 20141228004020.bcs). You should be able to figure out what your main database file is by looking at the size and timestamp for the file. If you are unsure, you can see which file you are loading the data from within the BC app. Go to Settings -> DB to see which is your current data file. It will also give you statistics on any other data file listed on your device.
If you replace your database file (e.g. 20141228004020.bcs) here with another version you will effectively be restoring the database from the version you replaced it with. Do this with caution because overwriting this file cannot be undone. Force the application to close before transferring that file. If the application is already open, it won't know to re-read the file that was placed there. You may also change the name of your database file before copying it in. As long as you don't change the suffix of the file ('bcs' or 'sqlite)', Book Crawler will know how to read it. You can select an alternate file under Settings -> DB;