The use of social media has become a regular habit for many and has changed the way people interact with each other. In this article, we focus on analysing whether news headlines support tweets and whether reviews are deceptive by analysing the interaction or the influence that these texts have on the others, thus exploiting contextual information. Concretely, we define a deep learning method for Relation-based Argument Mining to extract argumentative relations of attack and support. We then use this method for determining whether news articles support tweets, a useful task in fact-checking settings, where determining agreement towards a statement is a useful step towards determining its truthfulness. Furthermore we use our method for extracting Bipolar Argumentation Frameworks from reviews to help detect whether they are deceptive. We show experimentally that our method performs well in both settings. In particular, in the case of deception detection, our method contributes a novel argumentative feature that, when used in combination with other features in standard supervised classifiers, outperforms the latter even on small datasets.