In the paper Batch Normalization,Sergey et al,2015. proposed Inception-v1 architecture which is a variant of the GoogleNet in the paper Going deeper with convolutions, and in the meanwhile they introduced Batch Normalization to Inception(BN-Inception).
The main difference to the network described in (Szegedy et al.,2014)
is that the 5x5 convolutional layers are replaced by two consecutive
layer of 3x3 convolutions with up to 128 filters.
And in the paper Rethinking the Inception Architecture for Computer Vision, the authors proposed Inception-v2 and Inception-v3.
In the Inception-v2, they introduced Factorization(factorize convolutions into smaller convolutions) and some minor change into Inception-v1.
Note that we have factorized the traditional 7x7 convolution into
three 3x3 convolutions
As for Inception-v3, it is a variant of Inception-v2 which adds BN-auxiliary.
BN auxiliary refers to the version in which the fully connected layer of the auxiliary classifier is also-normalized, not just convolutions. We are refering to the model [Inception-v2 + BN auxiliary] as Inception-v3.