Hi. 

I want to have a different logo regarding the page I'm displaying.
Basically, I need to have a blue logo on homepage and a white one on the other. 
Is there an easy way to do that?

Many thanks.

I found out eventually. 
I post the solution here if someone has the same concern. 

If you want a different logo for your homepage :

1- upload file in /img/  (logo-hp.png)

2- Go to MySQL, in ps_configuration, copy PS_LOGO field, change PS_LOGO to PS_LOGO_HP and name of the logo by your new one.

3- Go to classes/controller/FrontController.php.
   Copy the whole page then go to override/classes/controller and create a FrontController.php and paste everything.

4- Go to line #1619 and add :

$logo_hp = $this->context->link->getMediaLink (_PS_IMG_.Configuration::get('PS_LOGO_HP'));

5- Below, you should see 

'logo_url'          => $logo

Change to 

'logo_url'          => $logo,
'logo_hp_url'       => $logo_hp

6- Finally, go to /themes/newyork/header.tpl, line 114 and change 

src="{logo_url}" 

with :

src="{if $page_name=="index"}{$logo_hp_url}{else}{$logo_url}{/if}"

Hope it'll help someone.