Legend · 4 tellings · Pan-India, South India, West India
The burning of the three cities
The gods build Shiva a cosmic chariot with Brahma as charioteer and Vishnu as the arrow to destroy the three cities of Taraka's sons; the Shaiva prelude has Vishnu send a heretical teacher to strip the cities of merit, while the Bhagavata has Vishnu as a cow and Brahma as a calf drink the demons' reviving well dry.
In the Shaiva telling the cities cannot be touched while their people keep the Vedic path, so Vishnu first conjures a teacher — named Arihat, with four disciples — who preaches a doctrine set against the Vedas and draws the citizens away from their rites, and Narada, himself converted, carries the teaching to Vidyunmali. Their merit gone, the demons are exposed. The gods then assemble Shiva's chariot with Brahma driving and Vishnu as the arrow, and Shiva burns the cities with a single shot as they align. In this frame Vishnu is the moral cause of the fall and Shiva the physical one. The same deluder motif recurs in the Vishnu Purana's Mayamoha and in the Puranic reading of the Buddha as Vishnu's deluding avatar.
What is different here:
Base telling. Adds the heretical-teacher prelude; Vishnu's role is trickster as well as weapon.
The Bhagavata reverses the emphasis. Maya builds the demons three flying cities of gold, silver and iron; Shiva's arrows kill the defenders, but Maya revives them in a well of nectar. So Vishnu becomes a cow and Brahma a calf and together they drink the well dry. Vishnu then provides Shiva with everything he needs — chariot, charioteer, banner, horses, elephants, bow, shield and arrows — and at noon Shiva burns the three residences and is called Tripurari. No heretical teacher appears.
What is different here:
No deluding teacher; Vishnu and Brahma as cow and calf drain the reviving well, and Vishnu supplies the whole arsenal; Shiva executes.
Tamil Shaiva tradition holds that Shiva needed no arrow at all and burned the three cities with a mere smile, which gives him the name Sirithu Purameritha Peruman, 'the lord who burned the cities laughing'. A Vedic seed already exists in the Taittiriya Samhita, where the gods forge an arrow with Agni as its point, Soma as its socket and Vishnu as its shaft for Rudra to shoot.
What is different here:
The chariot and arrow are dispensed with; Shiva's smile is the weapon.
The Kailasa temple at Ellora carves the archer twice, at the gateway and in the eastern gallery, with Brahma shown as his charioteer; Pattadakal has examples from the sixth and seventh centuries, and Hoysala and Vijayanagara temples repeat the four-armed archer with the Pashupata weapon.
What is different here:
Iconographic version; Brahma's role as driver is what the carvers show.
Sources: Tripurasura — Wikipedia; Tripurantaka — Wikipedia; The Buddha in Hinduism — Wikipedia; Srimad-Bhagavatam (Bhaktivedanta Vedabase), cited by canto.chapter; Manifestation of the unmanifested: Shiva sculptures of the Kailash temple, Ellora — Sahapedia