The Duchy of Amalfi was a state in Southern Italy between 700s and the year 1000. Formally a Byzantine vassal, the duchy has been ruled by Lombard princes. Despite its size anyway, (it covered Amalfi and the immediate region around it) it soon grew to become an economic powerhouse. Amalfi founded trade colonies everywhere in the Mediterranean, it even founded the first trade colony in Constantinople of the world. The Tavole Amalfitane were for most of the Middle Ages the main maritime code and to Amalfi we owe the invention of the compass (probably. The origin of the invention is disputed). It was, in few words, an undeniably important state, despite its sheer size. Now, this AH is about: What if the duchy doesn't fall to the Normans in 1073? Amalfi had all the potential of being a regional power: It had a big income from trade to which afford an army of mercenaries and a vast naval experience with which dominate the waves of the Mediterranean. The main POD is between 981 and 983. During this time, the Duke of Amalfi, Manso I, ruled the Principality of Salerno, a surely bigger, more populous state. So, Manso's domains covered most of southern Italy.
Anyway, due to harsh rule, Manso I was overthrown by the people of Salerno, who elected a new prince. Now, the "what if" is: What if Manso I ruled in a good, acceptable way the Principality of Salerno? With not one, but three important ports, the ports of Amalfi, Salerno and Taranto, Manso I rules a regional superpower, able to stand against opponents such as the Byzantines, the Pope, the Arabs in Sicily and the Emperor of the Holy Roman Empire. This will be a TL about his staying in power and about the post-Manso I period.
981-983: POD. Manso I, instead of harshly ruling the Principality of Salerno, governs it in an acceptable way.
983: No overthrowing of Manso I. In the east, the Khazar Empire falls.
985: Vikings start the colonization of Greenland, a green land at the time.
987: Baptism of the Rus of Kiev. War with Eastern Roman Empire.
999-1040s: Normans arrive in Southern Italy. They're initially used as bodyguards, to guard pilgrims returning from the Holy Lands, etc. Soon, they become mercenaries working for the Eastern Roman Catapan of Italy to put down anti-Byzantine revolts.
1004: Manso I dies. John I goes to the throne.
1007: John I dies. Sergio II becomes Duke of Amalfi, and is crowned Sergio III of Salerno. (Tto be continued. I accept suggestions.)