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Upgrading from version 3.5 or later involves dumping your Bedework database using the dump/restore utility and then restoring the file into the new version using the method outlined in 3.6 Chapter 2, “Bedework Basics”.
Upgrading from an earlier version of Bedework older than 3.5 uses the same process, but for public calendaring requires some post-processing of the data to migrate from a multiple calendar model to a single calendar model. A rudimentary script is available in bedework/projects/bwtools to help with this process.