Where are you and could you show us some pictures of your Peonies? As a general rule, Peonies should be divided and transplanted in fall with the eyes (buds for the next year growth) just under the ground level.

Well I'm not from USA or canada. I don't really have the pictures as they didn't bloom and I go to my garden on weekends as it's not in the city . It seems the ground has sat after the rainfalls and the eyes were partially showing above the ground in march. I did transplant them in fall, in October to be specific. The temperature in winter is variable, it can be anywhere from 19 to 50 F (global warming really does wreak havoc) to 105F in Summer. I don't really understand why it wouldn't bloom either. I panted it together with other peony I bought this one and the other the vendor was going to throw away as it was small and deemed unworthy to be sold. so I took it for free. funnily enough that one is blooming (bloomed the very first year) and this one just doesn't want to.

This is common when you divide a peony. The roots just aren't strong enough to support all the buds that were already forming when you divided it last fall. They may do the same next year so don't be surprised. By the third year, it should bloom normally.