Text attribute transfer is modifying certain linguistic attributes (e.g. sentiment, style, authorship, etc.) of a sentence and transforming them from one type to another. In this paper, we aim to analyze and interpret what is changed during the transfer process. We start from the observation that in many existing models and datasets, certain words within a sentence play important roles in determining the sentence attribute class. These words are referred to as textit{the Pivot Words}. Based on these pivot words, we propose a lexical analysis framework, textit{the Pivot Analysis}, to quantitatively analyze the effects of these words in text attribute classification and transfer. We apply this framework to existing datasets and models and show that: (1) the pivot words are strong features for the classification of sentence attributes; (2) to change the attribute of a sentence, many datasets only requires to change certain pivot words; (3) consequently, many transfer models only perform the lexical-level modification, while leaving higher-level sentence structures unchanged. Our work provides an in-depth understanding of linguistic attribute transfer and further identifies the future requirements and challenges of this taskfootnote{Our code can be found at https://github.com/FranxYao/pivot_analysis}.