The capsule includes a lower cap with a security strip which inserts removably on a mouth of a bottle. The upper part of the lower cap is open and provided with a neck which couples with an upper cap, also having a security strip. A reservoir is provided within the upper cap and has a breakable bottom; the reservoir also internally includes a cutter. The upper cap can move axially downwards with respect to the neck and the bottle, while it is prevented from moving upwards. The capsule also includes an anchoring between the reservoir and the neck of the capsule when the reservoir is inserted in the neck. The process includes filling the bottle with fizzy water, hermetically closing the bottle with a capsule containing substances to be added to the fizzy water, and introducing the substances into the fizzy water before consuming the drink.