The development of Cross continental cultural parallels including 

voluntary/honorary as well as forced/humiliatory or abject sacrifice,  as public spectacle occurring on stepped pyramidal architecture (in predominantly red) with plazas.  ritual combat with losers as sacrificial victims as Moche and Aztec.  Throwing/dropping.tumbling down of newly killed sacrificial victims from such pyramids as Maya or Aztec or rock cliffs  as the Moche in Peru.   Temple complexes with two primary pyramids, major and minor  (i.e. the Moche Huaca del Sol vs. Huaca de Luna as in Peru vs  Teotihuacan Pyramide del Sol & Pyramide de la Luna, or even Emerald Mound though the two are facing each other rather than at near right angles to each other as with the other two).   Rectangular wedding cake style of Stepped Pyramidal construction from Teotihuacan and Monte Alban in Mesoamerica to even the Akapana pyramid of Tiwanaku in Bolivia, which was created with large stone slabs creating inward slanting outer surfaces for each level.  

parallels of dress and adornment as nose rings, extremely large spreading and tall gold headgear, cranial deformation, skeleton head necklaces (aguateca shell necklace MN 15359,  house of the scribe) ,

animal-animal and animal-human combinations/merging/transformations/sculptural and ceramic representations especially involving feline/bird/serpent/human combinations and transformations.

Special prominence of Jaguar/feline as sculpted in large preclassical stone monuments, Peru chavin-cupisnique,  olmec in Guerrero as in ballcourt relief at Teopantecuanitlan vs. Raimondi stelae slab with pouting jaguar-humanoid face holding sprouting corn husks in each hand close to chest, along with other parallels such as sunken rectangular courts with feline/humanoid protruding heads in various degrees of (shamanic?) transformation.

 Not simply the ample use of use of skull symbolism as representing venerated gods and spirits and not evil or death fearfully, and use of multiple skulls as religious artistic elements such as Skull arrays such as otherwise 'Wall of Skulls' at the Tzompantli shrine at the Aztec Templo Mayor.    

Sculptural symbolism of serpent/feline or other tubular bodied being with heads at both ends in combination with human figures or as part of a larger sculptural element.    

Prominence of Twins in formative, cosmological myths among Inca, Maya, Aztec, and throughout tribes of Central and South America.

Trial and error of the gods in the making of humans, and not omniscent, omnipresent, nor omnipotent. 

Belief in deformity as a sign of divinity, as in Palenque's rulers,  Lord Pacal(born AD 603)'s beheaded uncle's clubfoot was considered a divine attribute.  Pacal's mother had an enlarged skull from acromegaly also considered divine.  Pacal flaunted his own clubfoot of proof of his divine desceent and the clubfoot was symbolized in maya art as a serpent and symbol of rulership at Palenque--blue guide p796.  Likewise in the Andes, the Moche and Inka saw deformities not only human but plant mutations or abnormalities as divine; branching, split, multiknobbed and odd shaped cobbs and potatoes considered sacred.

Large stone slab incised stone slab images of monte alban danzantes sacrificial victims and Cerro Sechin warriors and sacrificial victims and Palenque palace stone slabs in the inner courtyard of prisoners.   

Similar in basic chromatic aesthetic conception of bold polychrome designs (as Tikal Mundo Perdido Polychrome bowl with lid MN 11131)  

Similar smooth painted red/black/white Cups/mugs Inca like those of Maya. 

Intricate textile designs, weaving, bold coloring, geometric and figurative combined shared by meso and south america, with climate effecting the preservation of samples limited primarily to south american arid regions but confirmed indirectly by ceramic and mural depictions in meso america, and the continuation of unique living indigenous mesoamerican textile traditions, such as dress worn in Mayan regions to this day.      

The totemic pillar, which represents primarily one entity, one god, one king, which unlike the obelisk, the ashokan pillar, the trajan column, represents not a message, an edict, a commemoration, or a triumph, but an idol which preserves the fundamental cylindrical or square form of the material intentionally.  In this sense, the monuments of mayan Qurigua, the wooden pole of pachacamac, or other wooden figures of peru as at the MAP Larco museum of Cuzco, the stone lanzon of chavin, the totem poles of the pacific NW of North America, however distant and diverse in meaning and style, and closer in meaning and form to each other than those of Egypt, Mesopotamia, Persia, Greece, or Rome.