There is an upward trend in the influence of father's education on all three transitions. More exactly, there was an upward trend, although it's not clear that it's continued in the last couple of generations.
This figure shows the next two--attending college and graduating from college given that you attended. Again, both show an upward trend.
There's one more transition--getting graduate education--but the effect of father's education is near zero in all generations. That is, if you've graduated from college, how much education your father has doesn't predict whether you will get graduate education.
That raises the question of why would there be a trend over a 100 year period, through depressions, prosperity, declining economic inequality, rising economic inequality, urbanization, suburbanization, etc?