The Canon of Kings was a dated list of kings used by ancient astronomers as a convenient means to date astronomical phenomena, such as eclipses. The Canon was preserved by the astronomer Claudius Ptolemy, and is thus sometimes's called Ptolemy's Canon. It is one of the most important bases for our knowledge of ancient chronology.
The Canon only deals in whole years. Thus, monarchs who reigned for less than one year are not listed, and only one monarch is listed in any year with multiple monarchs. Usually, the overlapping year is given to the monarch who died in that year, but not always. Note that both periods where no king is listed represent times when Sennacherib, King of Assyria, held effective control over Babylon. His name is not listed because of the hatred the Babylonians held for him due to his destruction of the city in 689 BC.
The Canon is generally considered by historianscitation needed to be extremely accurate. The dates have been confirmed to be essentially accurate whenever they are checked against independent sourcescitation needed. Thus, the vast majority of historians and archaeologists view Babylonian chronology back to 747 BC as settled.