chop the tomatoes in large pieces
chop the garlic and the chilli pepper into fine pieces.
Cut the anchovies into pieces.
Heat olive oil (you can use some of the oil of the anchovies) in a pan.
Bake the garlic and the chili pepper for two minutes.
Extinguish with the white wine.
Let it reduce a bit, and then add the tomatoes, anchovies, black and green olives. Let it simmer for 10 minutes.
Meanwhile heat water and cook the linguini.
Cut the basilicum leaves into small pieces, and leave some of them for garnishing.
When cooked, drain the pasta and mix it with the sauce. Put some of the cooking water aside in case the sauce is too thick.
Add the basilicum, some lemon juice and pepper and salt tot taste.
Let it simmer a few more minutes so that the flavours can integrate, and then serve immediately.