Steve,
Be more gradual about it.
The first interval should take your HR about 2-3 mins to reach zone 4. Every interval after that you will be more warmed up and HR will rise more quickly. Avoid sprinting the first part of the interval to get your HR up but rather focus on applying even force to the pedals the whole interval. In the final interval your HR should reach zone 4 in 45 – 60 seconds.
Lynda