Your answers when White avoids the Open Sicilian: the Alapin (2.c3 Nf6), the Closed and Grand Prix (…Nc6, …g6), the Smith-Morra, the Rossolimo (3.Bb5 g6) and the Moscow (3.Bb5+ Bd7). This is a intermediate opening course for Black (ECO B20), written for players rated around 1600. Each move is explained and then drilled on a board; it is free.
Key ideas of Anti-Sicilians for Black
Against 2.c3 play 2...Nf6: after e5 Nd5 the knight is safe and the e5 pawn becomes a target.
Against 2.Nc3 and f4, the fianchetto (...g6, ...Bg7) and ...Nd4 meet White's attack.
Against the Rossolimo (3.Bb5), ...g6 and ...Bg7 give the bishop pair if White takes on c6.
Against the Moscow (3.Bb5+), ...Bd7 trades the attacking bishop and Black is comfortable.
If White plays d4 after all, take on d4 and you are in your Open Sicilian course.
The line trainer
The line trainer for Anti-Sicilians for Black has 50 lines that grow out of 1. e4 c5, learned a few new ones a day with spaced-repetition review.
chessGM