Make the sauce: In a saucepan combine the tomatoes with the juice, the bell pepper, the garlic, the onions, and the stock. Bring the liquid to a boil and simmer the mixture, covered, stirring occasionally, for 30 to 40 minutes, or until the vegetables are very tender. Force the mixture through a food mill fitted with the medium disk into another saucepan, add salt and pepper to taste, and simmer the sauce until it is reduced to about 2 1/2 cups.
Make the filling: In a bowl combine well the Parmesan, the mozzarella, the ricotta, the chives, and salt and pepper to taste.
Roll out the dough on a pasta machine one sheet at a time, while assembling the ravioli. After rolling out 1 sheet of dough, trim the ends. Dust both sides of the dough with flour, feed the dough carefully through the rollers set at the fifth-lowest notch, and continue to feed it through the rollers, turning the dial one notch lower each time, until the second lowest notch is reached. Trim the ends of the dough and cut the dough crosswise into 2 pieces, 1 piece 1 1/2 inches longer than the other.
Put heaping tablespoons of the filling in lengthwise rows on the shorter piece, spacing them about 1 inch from the edges with their centers about 3 inches apart. Brush the dough around the filling with water, put the longer piece of dough on top, and press it gently around the mounds of filling, pressing out any air bubbles. With a fluted pastry wheel or knife cut the dough between the rows of filling into about 2 1/2- by-2-inch rectangles. Arrange the ravioli as they are formed in one layer on a lightly floured tray. Continue to make ravioli, 1 sheet of dough at a time, with the remaining dough and filling in the same manner. The ravioli may be kept, uncovered and chilled for up to 2 hours.
To 2 kettles of boiling salted water add the ravioli and cook them at a bare simmer, covered partially, for 10 to 12 minutes, or until they are al dente. Divide the sauce, heated, among 4 heated dinner plates and arrange the ravioli on the plates. Garnish each portion with some chopped chives and serve the ravioli with the Parmesan.