In a small saucepan over high heat, bring 2 cups of cranberries, blackberries and water to a boil. Simmer until fruit bursts, about 15 minutes. Mash fruit and strain through a sieve. Refrigerate until completely chilled (about 1 hour).
In a pitcher, combine fruit purée, remaining cranberries, apple must and carbonated water, then pour into glasses with ice cubes and a sprig of rosemary to serve.