Now add the octopus, head down, and cover. Let the octopus simmer over gentle heat for about 15 minutes.
Uncover the pot. The octopus should have given off a fair amount of liquid. Pour the tomatoes, olives and capers and re-cover tightly. (You can use some parchment paper or aluminum foil to create a better seal if you like.) Simmer the octopus gently until tender, about 30-45 minutes.
Mix in the minced parsley leaves, give the pot a turn, and let it sit for five minutes.
Serve your polpo alla luciana warm, with a nice chunk of crusty bread to soak up those delicious juices.