In a large pot, heat oil over medium heat. Add sausage and cook on each side to brown. (The sausage does not have to cook thoroughly as it will be added to the sauce to simmer for additional time.)

Remove sausage from the pan and set aside. Add onion and garlic to pan and saute until the onion is translucent (about 3 minutes). Add crushed tomatoes and spices. Slice the sausage into 1/2-inch-thick pieces, place back in the pan, then let it simmer.

Meanwhile, cook pasta according to package instructions. Save 1 cup of the pasta water. Drain the pasta.

Add the pasta to the sauce and mix well. Turn the heat to medium heat and add the pasta water as needed to maintain a good sauce consistency. Add the sliced peppers and olives, then cook for 10 minutes or until peppers are softened.