Dissolve yeast in water. Pour flour into a mound onto the counter. Add dissolved yeast, salt, and olive oil to center. Work in flour from outside into liquid with fork until it resembles a dough. Work in rest of flour by hand. Leave 1 tablespoon flour unincorporated. Place dough in bowl. Sprinkle with leftover flour. Cover with dishtowel. Let rest for about 1 hour at room temperature, until double in size.
Pass tomatoes through food mill using smallest holes into small bowl. Set aside.
When dough is ready, place heavy aluminum foil on a pizza board. Oil it with 1 tablespoon olive oil. Spread dough on foil, using fingertips to about 16 inches by 14 inches. Spread on pureed tomatoes. Sprinkle on mozzarella. Distribute anchovies and capers. Add salt, pepper, and oregano. Drizzle on remaining 1 1/2 tablespoons olive oil.
Bake on middle shelf for 35 minutes or until crisp. Remove. Slice and serve.