To get a general idea of how EAS, IAS (or CAS), TAS and Mach vary with altitude in the ISA below the tropopause, just hold your right hand out in front of your face so that you see the palm of your hand, and your fingers point upwards. Now spread out your fingers.
Your little fnger represents EAS, the one next to it IAS (or CAS), the next one is TAS and the next is Mach. The palm of you hand represents low altitude and your fingertips represent high altitude. The left edge of your palm is low speed values and the right edge is high speed values.
To see what happens in a constant IAS (or CAS) climb rotate your hand so that the IAS (or CAS) finger points straight upwards. The directions of the other fingers show how the other speeds vary. You little finger is sloping left indicating that EAS is decreasing. The other two fingers are sloping right indicating that TAS and Mach are increasing. So in a constant IAS climb the EAS decreases and the TAS and mach number both inrease.
Now rotate your hand so that the Mach finger points straight upwards. All of the other fingers are sloping left indicating decreasing EAS, IAS and TAS. So in a constant mach climb in the ISA below the tropopause, all of the other speeds decrease.
Maximum allowable speed at low altitude is limited by VMO which is a CAS. Maximum allowable speed at high altitude is limited by MMO which is a mach number.
To avoid exceeding either of these limits jet aircraft climb schedules are specified in terms of CAS and Mach number. For example 270 Kts / M0.8. This means that the climb is initially at a constant 270 Kts CAS.
As altitude increases at this constant CAS, the mach number gradually increases. The crossover altitude in this case is the altitude at which the 270 kts CAS is equal to Mach 0.8. When this altitude is reached the climb switches to one of constant mach number at Mach 0.8.
During the constant CAS part of the climb the TAS is increasing. During the constant Mach part the TAS is decreasing. So the greatest TAS occurs at the crossover. Assuming still air or constant wind speeds at all altitudes, this means that greatest groundspeed in the climb occurs at the crossover altitude.