Mix sugar and water in a large saucepan over medium-high heat. Stir occasionally until the sugar has dissolved completely, about 7 minutes. Meanwhile, wash apricots and remove stones; finely chop the flesh.
Add the chopped apricots to the sugar and water mixture. Reduce heat to medium. Cook until the apricots have liquefied, stirring and mashing constantly. Remove from heat and let cool.
Pour Prosecco into the cooled apricot mixture; it will bubble and double in volume. Gently stir until fully incorporated and the bubbles have reduced slightly.
Pour the mixture into a freezer-safe container and cover. Freeze until mixture begins to solidify, 1 to 2 hours, depending on your freezer. Scrape down the sides and mix the granita using a fork. Repeat every 30 minutes until the granita has become course and grainy, about 6 hours. Do not shake the container instead of scraping it with a fork; it is the action of scraping that forms the characteristic crystals that make granita unique.
Scrape the granita into 8 serving dishes using a large spoon. Top with pomegranate seeds. Serve immediately.
If you can't find red blush apricots, use regular ones.