Boil 500 ml water. Remove from heat, stir in tea and agave syrup. Let tea steep for about 8 minutes. In the meantime wash and drain the blackberries. Wash limes hot, drain, cut in half and cut into pieces.
Pour tea through a fine sieve into a bottle and let it cool down. For the preparation of blackberries and limes, divide into 6 glasses (each containing approx. 400 ml). Press down with a pestle, fill up with tea and mineral water.