Active learning (AL) aims to reduce labeling costs by querying the examples most beneficial for model learning. While the effectiveness of AL for fine-tuning transformer-based pre-trained language models (PLMs) has been demonstrated, it is less clear to what extent the AL gains obtained with one model transfer to others. We consider the problem of transferability of actively acquired datasets in text classification and investigate whether AL gains persist when a dataset built using AL coupled with a specific PLM is used to train a different PLM. We link the AL dataset transferability to the similarity of instances queried by the different PLMs and show that AL methods with similar acquisition sequences produce highly transferable datasets regardless of the models used. Additionally, we show that the similarity of acquisition sequences is influenced more by the choice of the AL method than the choice of the model.