The best transition word or phrase to clarify the relationship between the ideas in the sentences is "as a result." This indicates a cause-and-effect relationship, showing that the tendency to travel during holidays leads to increased lines at airports and traffic jams. Therefore, the correct sentence would be:
"People often tend to travel around holidays because they want to spend time with their families; as a result, the lines at airports and traffic jams in big cities definitively increase in the days leading up to a big holiday."