I'm not sure about the others, but for Mesoamerican history the "ages" are divided into distinct periods that don't really correspond with the Old World except in some cases.

The first is the Paleo-Indian period could roughly be considered similar to the Paleolithic, in that agriculture wasn't practiced and people mostly lived in smaller, mobile groups. This lasted from the beginnings of human habitation on the continent until about 3500 BCE.

The second is the Archaic, lasting until around 2000 BCE, which cooresponds roughly to the Neolithic in that it's the beginnings of agriculture and pottery. People started settling down. This and the previous period correspond with the Old World because global climate patterns were similar. Farming became attractive around the world as it warmed following the Ice Age.

The third is the Formative, lasting until around 250 CE. Mesoamericans never developed metal tools, so the metal eras can't be compared. During this era, however, you see the beginnings of large states. The Olmecs, the Zapotecs at Monte Alban, and numerous Mayan sites such as El Mirador, Izapa, Kaminaljuyu, and more. Writing, large-scale intensive farming, the ritual and daily calendars, and many more iconographic and religious elements were developed in this period.

The next is the Classic period, lasting until around 900 CE. This period coincides with the flowering of Teotihuacan, the Classic Maya, and Tula. Teotihuacan dominates the Valley of Mexico during the beginning, and Tula towards the end. During this period there seem to have been large scale migrations of Nahuatl speaking people from the North, who reached as far as Nicaragua. They settled throughout Mesoamerica and were apparently responsible for the rise and fall of numerous civilizations. The migrations may have contributed to the end of the Classic Maya, whose cities were abandoned at the end of this period. The period's close is closely associated with the end of the Classic Maya, though Mayan Civilization continued throughout the Yucatan peninsula in other sites.

The remainder of Pre-Hispanic Mesoamerican chronology is known as the Postclassic period, and it lasts until 13 August 1521, the date of the fall of Tenochtitlan. This is obviously not the end of Mesoamerican history, but it is the end of the historical era as recorded by historians. Much of the Postclassic is dominated by the Nahuas who migrated in during the Classic period. Tula is the preeminent city in Central Mexico during the end of the classic until around 1200 CE, when city states around the Valley of Mexico begin to rise. Eventually a triple alliance of Tenochtitlan, Texcoco, and Tlacopan gain power and conquer the others. These are the people we call the Aztecs, though they wouldn't have recognized the label. In the Maya area there are cities such as Chichen Itza, Mayapan, and numerous others. Tulum, the famous seaside resort town, is known to have been inhabited through the conquest.

So as you can see, these eras don't really coorespond to those of the Old World. Mesoamerican technology took off in different directions due to their different needs and available resources (no pack animals = no need for a wheel). The eras are divided based on cultural and political developments, especially related to those at key sites such as Teotihuacan, Tula, San Lorenzo, La Venta, and numerous ones in the Maya area.