LLMs have been extensively used for the task of automated code generation. In this work, we examine the applicability of LLMs for the related but relatively unexplored task of code-equivalence checking, i.e., given two programs, whether they are functionally equivalent or not. This is an important problem since benchmarking code equivalence can play a critical role in evaluating LLM capabilities for tasks such as code re-writing and code translation. Towards this end, we present CETBench - Code Equivalence with Transformations Benchmark, constructed via a repository of programs, where two programs in the repository may be solving the same or different tasks. Each instance in our dataset is obtained by taking a pair of programs in the repository and applying a random series of pre-defined code transformations, resulting in (non-)equivalent pairs. Our analysis on this dataset reveals a surprising finding that very simple code transformations in the underlying pair of programs can result in a significant drop in performance of SOTA LLMs for the task of code-equivalence checking. To remedy this, we present a simple fine-tuning-based approach to boost LLM performance on the transformed pairs of programs. Our approach for dataset generation is generic, and can be used with repositories with varying program difficulty levels and allows for applying varying numbers as well as kinds of transformations. In our experiments, we perform ablations over the difficulty level of original programs, as well as the kind of transformations used in generating pairs for equivalence checking. Our analysis presents deep insights into the working of LLMs for the task of code-equivalence, and points to the fact that they may still be far from what could be termed as a semantic understanding of the underlying code.