Ah shite, sorry skip. I have no idea about the authenticity of this, but authenticity often stands in the way of a good meal anyway.
For putanesca I put a pan on to boil for the pasta first and a frying pan or another saucepan second. While waiting for the water, the oil from the anchovies goes into the frying pan at medium-high heat, followed shortly after by a minced clove of garlic per person, plus one more for the pan. A minute later, a pinch of red pepper flakes and black pepper, and the anchovies themselves, which are crushed apart with the wooden spoon in the pan. This is all fried together with occasional agitation until the anchovies have essentially disappeared, and in the meantime, I have been pressing the stones from the olives, if necessary, and if not, I will start slicing up a couple of tomatoes, or a handful of cherry tomatoes. Once the anchovies are gone-ish, I add the olives, wait a minute, add some capers, wait another minute, add some chopped parsley and wait yet another minute, then finally add the tomatoes, which are crushed down and simmered for 60 seconds. I use fresh tomatoes instead of a tin because I don't think this is a pasta-in-sauce dish, it should instead be things-stuck-to-pasta. You could get the same effect by using just a third of a tin or so.
By now the pasta is about three-quarters on the way to being done, so it gets drained and a mug full of the cooking water is retained (anyone with the counterspace available in their kitchen might like to use a ladle of the hot water to preheat the bowls they'll be eating from, which may or may not be necessary depending on the time of year and how warm your house is). The pasta is tossed into the sauce along with some of the reserved cooking water, stirred and simmered with more water as needed until the pasta is cooked, then a squirt of the good olive oil is tossed through at the last possible second, emulsifying the sauce and giving it a glossy sheen. A knob of butter does the same thing.
Slop into your (hot?) bowls, add any finishes you want (parmesan or pecorino, chopped herbs or rocket, fresh chopped chilli or dry chilli flakes, garlic-toasted pangrattato, etc.).
Sometimes I grate a bit of lemon zest into it somewhere along the line if there's one lying around on the counter.