Pros

+ Escape with Arcane Shift
+ Very good skillset
+ Team Steroid Essence Flux
+ Personal Steroid Rising Spell Force
+ Good Early, Mid and Late game damage
+ High Skillcap

Cons

- No Crowd-Control
- Difficult to master
- 3/4 Attacks are Skillshots
- Squishy like all ADs
- Highly focused
- Needs a lot of Gold

There is nothing much to say. It is a ADC so there is not too much different things here. But Most of the skills deal Magical Damage so it is good to have some Masteries can support skill damage.

All of these items have a common value: They are blue colored.
But really WHY is it that much neccessary to build Ezreal like that ?
I will tell you:

Blue Items supports your mana and mana regeneration so you will not need to go for the blue buff and you can leave it for your jungler.
You will need a good attack damage as an ADC but your main power will be your skills.
You will be maxing your skills with the order of Q-W-E (ad based skill first, main harrass skill second and escaping skill third) so you will need AD for your play style.
Your game is spam dependent, you must change your instant using thing from SHIFT + Q,
W, E to Q, W, E for rapid skill shots. This will also help you getting better with all skill shots.
While spmamming, your Q will decrease the cool downs so you will lose lots of mana in an instant, Blue items will restore your mana and let you do a good damage with your spam.
Your main stats are AD, Mana, Mana Regeneration. Your second stats are AS, Penatration, Life Steal. So you will need items giving these stats at the same time, Iceborn Gauntlet is needed for the passive, it also gives you a great deal of mana and a little with ability power.
You will be collecting the Elder Lizard first for farming. They will be trying to find an opening to attack/farm, and this item will close your biggest opening. It will earn you time from farming. It will also give you enough mana regeneration and AD before your main item Manamune.