Pasta dough made with eggs is more typical of Northern Italy (often times with a higher ratio of egg yolks rather than the whole eggs that I’m using in my recipe below), while 2-ingredient pasta dough made from just semolina and water is more typical of parts of Southern Italy.
Yes, to make eggless fresh pasta, just omit the eggs called for in the recipe below and replace them with about 1 to 1 ¼ cups room temperature water. Pasta dough made with eggs is more typical of Northern Italy (often times with a higher ratio of egg yolks rather than the whole eggs that I’m using in my recipe below), while 2-ingredient pasta dough made from just semolina and water is more typical of parts of Southern Italy. Each region has its own pasta shapes and type of dough that is popular and I’m not claiming that my recipe is authentic in any way. It’s just what I have found easiest to work with!