Once sage Atri - the Maanas Putra of Brahmaa went to do penance at the bank of the river Nivindhya which flew by the foothills of Trayakshakul mountain as per the instructions of Brahmaa himself. The effects of Sage Atri's penance were such that devastating flames of fire manifested from his head. The fire spread in all the three world in no time. The deities were terrified by the death and destruction caused by the fire in all the three worlds. They went to Brahmaa to seek his help. Brahmaa took them to Vishnu Jee and revealed to him about the destruction caused by the fire. All of them went to Shiv and told him everything. So Brahmaa, Vishnu and Shiv went to Atri Jee and blessed him. Atri recognized them. He eulogized them.

It is at some other time, that Atri's wife Anasooyaa gave birth to three sons, who in fact were the incarnations of Brahmaa, Vishnu and Shiv. Brahmaa's incarnation was Chandramaa (Moon), Vishnu incarnated as Dattaatreya and Shiv took incarnation as Durvaasaa.

My Note
There is also a different version of this legend. Once Atri had gone out and Atri's wife Anasooyaa was alone in her house. So the Tri-Moorti went to test the chastity of Anasooyaa. They went there in the guise of Braahman and asked for Bhikshaa (alms). When she wanted to go inside to bring Bhikshaa they told that they did not want the ordinary Bhikshaa. On asking what they wanted, they told that they wanted her to come naked before them. Anasooyaa got in a flux. So she said to them - "OK. let me go and take off my clothes." She went inside and started taking her clothes off praying her husband, Devtaa and Bhagavaan that "If I am a true Satee then these three Braahman should be transformed into newborn babies." She took off her clothes, and came out. She saw three newborn babies crying for milk. She breastfed them, satisfied them and went inside again. She wore her clothes and came out to find those three babies again in the guise of Braahman. Pleased with her Bhakti to her husband Braahman showed her their real form and asked her to ask for any Var (boon). She said - "If you are pleased with me then be my children forever." Then the three Dev took birth as Chandramaa (Brahmaa's incarnation), Dattaatreya (Vishnu's incarnation) and Durvaasaa (Shiv's incarnation).

Durvaasaa and King Ambareesh
Read their story in   Bhaagvat Puraan, 9/2

Durvaasaa had tested the religiousness and virtuosity of numerous people. He had also tested the religiousness of King Ambareesh, who ruled over Sapt Dweep - whole Prithvi. Once king Ambareesh had observed a fast on Ekaadashee. Next day, when he was about to break his fast sage Durvaasaa arrived accompanied by his large number of disciples. Durvasa was very furious with King Ambareesh. He said - "You had invited me for this particular day, but you have also insulted me by breaking the fast by drinking water in my absence." Durvaasaa would have burnt King Ambareesh to ashes by his curse, had not Sudarshan - the weapon of Vishnu, came to his rescue. Sudarshan then tried to burn sage Durvaasaa when suddenly a heavenly voice was heard from the sky which said - "Durvaasaa is no one but the incarnation of Shiv himself." Hearing this Sudarshan's anger was pacified. King Ambareesh then begged his forgiveness from sage Durvaasaa.

Shiv Incarnates as Rishabh

After the churning of the Milky Ocean had been accomplished, numerous things had emerged out from the ocean. Jewels, Moon, Lakshmee, Poison, Uchchaishravaa horse, Airaavat elephant, Vessel containing Nectar were some of the things which emerged out from the ocean after the churning. A tremendous battle was fought between Devtaa and Asur to have control over the vessel containing Nectar. The Asur had snatched that vessel from the Devtaa and ran away with it. By the divine inspiration of Shiv, Vishnu appeared in the form of Mohinee - the enchanting beauty. He successfully recovered that vessel from the control of the demons.

To distract the attention of the demons from the nectar, Vishnu created numerous Apsaraa. When the demons saw them, they forcibly carried these Apsaraa to their abode - the Nether world. After that they again returned to take control of the Nectar. By that time, Vishnu had made the deities drink all the nectar. When the demons came to know about this, they became very furious and attacked the deities. A tremendous battle ensured between both the sides. Ultimately the demons got defeated. To save their lives the demon ran towards their abode. Vishnu chased the demons and entered the nether world. He killed many of the demons.

Vishnu then saw those enchanting beauties who had been abducted by the demons. Ironically Vishnu got infatuated by their beauty - who were His own creation. Vishnu remained there for a long time. During his stay in the nether world many sons were born to Vishnu. They were very wicked and cruel. These sons of Vishnu started tormenting the inhabitants of all the three worlds. All the deities and the sages went to Shiv to take his help. They requested him to kill the cruel sons of Vishnu and re-establish him (Vishnu) in his own abode, which He had abandoned for the Nether world.

Shiv went to the nether world in the form of an Ox (Vrishabh). He killed all the sons of Vishnu with his sharp horns. Seeing the death of His sons, Vishnu came forward to fight with Shiv. He attacked Shiv with his various weapons, but there was no affect on Shiv. Ultimately Vishnu was able to recognize him. He eulogized Shiv. Shiv then requested Vishnu to return to Vishnu Lok which He accepted. Vishnu left his 'Sudarshan Chakra' in the nether world and went to His own abode, where Shiv presented Him a new Sudarshan Chakra. So in the nether world there is still another Sudarshaa Chakra.