1) Why Social Networks icons change when I see the same page through different browsers (Firefox and Chrome)?
Please take a look at the following link using Firefox and Chrome:
2) How to fix it?
If you were using the default AddThis configuration it's using what we call Preferred Services. These are different for each individual based on their past sharing history and what services are most popular in our service. These are designed to increase sharing by showing users the services they use most often.
If you want to specify which services are displayed, you can do it by using a service code instead of preferred. Details are available here: http://www.addthis.com/help/client-api#rendering-preferred-services
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