In a large skillet, heat 2 tablespoons of the olive oil. Season the pork with salt and pepper and cook over moderately high heat until richly browned all over. Transfer the pork to the slow cooker, cover and turn it on to high. Add the remaining 1 tablespoon of olive oil to the skillet. Add the sausages and cook over moderate heat until browned all over, about 10 minutes. Transfer the sausages to the slow cooker.

Add the pancetta to the skillet and cook over moderate, stirring a few times until the fat has rendered, about 7 minutes. Add the onion, garlic and carrots and cook, stirring a few times, until softened, about 8 minutes. Add the red wine and stir to release any browned bits on the bottom of the skillet. Boil the wine over high heat until reduced by half, about 4 minutes. Add the tomatoes and their juices and the tomato puree and bring to a boil. Transfer the mixture to the slow cooker and add the thyme, rosemary and water.

Cover the slow cooker and cook on high for 2 hours. Transfer the sausages to a bowl and cover. Cook the sauce for about 2 hours longer, until the pork is very tender.

Transfer the pork to a bowl and shred coarsely with 2 forks. Coarsely break up the sausage. Return the meats to the cooker and simmer the sauce for 30 minutes longer. Discard the thyme and rosemary sprigs and season the sauce with salt and pepper.

Bring a large pot of salted water to a boil. Add the spaghetti and cook, stirring occasionally, until al dente. Drain the spaghetti and return it to the pot. Stir in half of the sauce. Transfer the spaghetti to a platter and top with the remaining sauce. Serve right away, passing cheese at the table.